Author details

adsorption of MB from the dye mixture is clear for the same reason of surface charge as discussed before. After adsorption and subjecting the dye solutions to illumination of simulated light, the degradation of MB was started (Figure 9b). According to postulates of any photocatalytic process, the catalyst will initially adsorb the reactant, catalyze the reaction, and finally leave the products. By the same concept, the adsorbed dye was degraded, while dyes in

Figure 8. Absorption spectra of MB dye (1 104 M) in presence of (a) Co-doped TNT 1 calcined at 500C for 2 h and (b)

Co-doped TNT 1 at Au in dark and under illumination [13] (copyright 2018, Elsevier).

the solution remained without effect [13].

32 Photocatalysts - Applications and Attributes

Ayman Hassan Zaki\* and Waleed Mohamed Ali. El Rouby

\*Address all correspondence to<EMAIL_ADDRESS>
Materials Science and Nanotechnology Department, Faculty of Postgraduate Studies for Advanced Sciences (PSAS), Beni-Suef University, Beni-Suef, Egypt


**Environmentally Friendly Polymers and Polymer Composites**

Edited by

Rafael Balart, Nestor Montanes, Franco Dominici, Sergio Torres-Giner and Teodomiro Boronat

Printed Edition of the Special Issue Published in *Materials*

www.mdpi.com/journal/materials


**2. Zucker diabetic fatty rats**

An animal model for biomedical investigation is one in which normative biology, behavior, and pathological process can be studied and in which the phenomenon in one or more respects resembles the same phenomenon in humans [35]. Research in diabetes on humans is not possible or only partially possible. Hence, animal model of DM is very useful and advantageous [36]. Animal disease models are essential tools for studying the pathophysiology of DM enabling therapeutic interventions to be developed [37]. It is true that the present therapeutic approaches to treat DM and obesity, which are saving many lives every day, were invented, validated, and optimized on animal models [38]. When studying T2DM the use of an animal model with a homogenous genetic background is advised [39]. Most of the available models are based on rodents [36]. Rodents are most commonly utilized due to their small size, short generation interval, and easy availability [39] and because of economic consideration [36]. Being mammals, the physiology of rats is similar to humans than nonmammalian species [40]. Nevertheless, nonrodent models of diabetes are needed as a valuable supplement to rodents for both practical and physiological reasons with respect to humans [36]. Many animal models for DM research are obese, reflecting the human condition where obesity is closely related to T2DM development [41]. Animals exhibiting a syndrome of insulin resistance

and T2DM reflecting the human disease involve many species with genetic, nutritional, or experimental causation [36]. There are a lot of rodent models available for the research in T2DM, but some of them may not always be satisfactory to mirror human T2DM due to the large heterogeneity in the latter. There are no fully unified classification criteria for this type of animal model. But, the spontaneous type 2 diabetic rodent models are considered the most outstanding and most useful [42].

According to Srinivasan and Ramarao [36], spontaneous diabetic animal models have special advantages and also disadvantages. The advantages are:

Among the disadvantages are mainly:

One of the rodent models that reflect human form of T2DM is Zucker diabetic fatty (ZDF) rats. ZDF rats as spontaneous diabetic animal model exhibit both the prediabetic and the end stage observed in human T2DM patients [43]. Spontaneously diabetic animals of T2DM may be acquired from the individuals with one or several genetic mutations transmitted from generation to generation or selected from nondiabetic outbred animals by repeated breeding through several generations. The result is that these animals inherited DM either as single or multigene defects. The metabolic particularities result from single gene defect (monogenic) which is due to dominant gene or recessive gene, or it can be of polygenic origin [36].

ZDF rats come from a colony of outbred Zucker rats in the laboratory of Dr. Walter Shaw at Eli Lilly Research Laboratories in Indianapolis (USA) during the years 1974–1975. In early 1981, some animals with diabetic lineage were designated and redefined. An inbred line of ZDF rats was established in 1985. Development to a genetic model was established in 1991 [44]. The Zucker fatty (ZF) rats carry a spontaneous mutation in the leptin receptor gene (fa) [45]. ZF rats resulted from the simple autosomal recessive (fa) gene on chromosome 5 [36]. This mutation causes hyperphagia, early onset of obesity, and insulin resistance [14] along with increased growth of subcutaneous fat depot [46]. At the age of 4 weeks, ZF rats gain weight more rapidly due to increased growth of subcutaneous fat depot, and

**79**

*Zucker Diabetic Fatty Rats for Research in Diabetes DOI: http://dx.doi.org/10.5772/intechopen.88161*

linemia [42].

they have a noticeably higher body weight at about the age of 9 weeks [47]. The hyperphagia and obesity in ZF rats are attributed to hypothalamic defect in leptin receptor signaling that is related to mild hyperglycemia, mild glucose intolerance, insulin resistance, hyperlipidemia, and moderate hypertension [46]. ZF rats have

Thereafter, a mutation in ZF strain led to a substrain with an evident diabetic phenotype—the Zucker diabetic fatty (ZDF) rats [42]. ZDF rats are less obese than ZF rats having a decrease beta cell mass which resulted in inability to compensate for severe insulin resistance [48]. The ZDF rats were derived by selective inbreeding of hyperglycemic ZF rats [49] within the first months of life due to leptin receptor defect and a genetically reduced insulin promoter activity [17]. ZF rats maintain normoglycemia despite their obese phenotype, hyperlipidemia, and hyperinsu-

The ZDF male rats became an experimental model for type 2 diabetes mellitus (T2DM). They have a predictable progression from prediabetic to diabetic state [50]. The ZDF rats carry a genetic defect in β-cell transcription. It is inherited independently of the leptin receptor mutation and insulin resistance [17]. In prediabetic stage of ZDF rats, there is no change in insulin mRNA levels. But, significant reduction (30–70%) of other islet mRNA levels, such as glucokinase, mitochondrial

Ca2+-ATPase, and transcription factor islet-1 may be detected [51]. It is known that FFA-induced suppression of insulin output in prediabetic stage of ZDF rats is conveyed by nitric oxide (NO) [52]. ZDF rats start to develop T2DM as early as 10 weeks of age, reaching 100% incidence at around 20 weeks of age [53]. It is possible to shorten prediabetic state and reach the symptoms of T2DM after high-energy diet. But, the animals receiving this diet are in the risky group because the diabetic state with its complications arrives quickly and rats can perish. In our experiment with ZDF rats, high-energy diet caused ketoacidosis that meant two cases of animal death

Blood glucose concentrations in ZDF rats usually increase from 7 to 10 weeks of age and impaired glucose tolerance at 5–7 weeks of age. At the age of 12 weeks, glucose intolerance becomes more severe than at 5–7 weeks of age [55]. Chronic and increasing hyperglycemia in ZDF rats is related to the loss of insulin and pancreatic duodenal homeobox (PDX-1) mRNAs. The lack of glucose stimulated insulin secretion. The possible prevention of hyperglycemia could block the deficit in insulin

Male ZDF rats that are homozygous recessive have nonfunctional leptin receptors (fa/fa) and develop hyperlipidemia, obesity, and hyperglycemia. Rats that are homozygous dominant (+/+) or heterozygous (fa/+) are lean with normoglycemia. They are healthy, display no symptoms of diabetes, and are usually used as agematch control rats in the experiments. In young fa/fa rats, insulin resistance appears which extends to a deployed insulin secretory defect that initiates hyperglycemia and inadequate β-cell compensation [17, 49]. The insulin resistance is a result of a

In ZDF rats, there are sex differences for phenotypes of diet-induced insulin resistance and glucose intolerance. The most affected are male individuals [57]. On normal diet, male rats from ZDF strain develop severe hypoinsulinemia and hyperglycemia by 4 months of age. Female individuals maintain normal level of blood glucose and insulin despite advanced obesity [38]. Female ZDF rats with fa/fa genotype become also obese and insulin resistant, but do not progress to hyperglycemia, except when fed a high-fat diet [58, 59]. The female

channels,

glycerol-3-phosphate dehydrogenase, voltage-dependent Ca2+ and K+

in 7th week after initializing feeding with this caloric diet [54].

mutant leptin receptor that causes obesity [17].

amount and PDX-1 gene expression and improve insulin secretion [56].

impaired glucose tolerance rather than apparent diabetes [42].

*Animal Models in Medicine and Biology*

multifactorial disease easy.

Among the disadvantages are mainly:

d.Require sophisticated maintenance.

and T2DM reflecting the human disease involve many species with genetic, nutritional, or experimental causation [36]. There are a lot of rodent models available for the research in T2DM, but some of them may not always be satisfactory to mirror human T2DM due to the large heterogeneity in the latter. There are no fully unified classification criteria for this type of animal model. But, the spontaneous type 2 diabetic rodent models are considered the most outstanding and most useful [42]. According to Srinivasan and Ramarao [36], spontaneous diabetic animal models

a.The development of T2DM is of spontaneous origin involving genetic factors.

c.Most of inbred animal model in which the genetic background is homogeneous and environmental factors can be controlled allow genetic dissection of this

a.Highly inbred, homogenous, and mostly monogenic inheritance and development of diabetes are highly genetically determined unlike heterogeneity in humans.

c.Mortality due to ketosis problem is high in the case of animals with brittle pancreas

One of the rodent models that reflect human form of T2DM is Zucker diabetic fatty (ZDF) rats. ZDF rats as spontaneous diabetic animal model exhibit both the prediabetic and the end stage observed in human T2DM patients [43]. Spontaneously diabetic animals of T2DM may be acquired from the individuals with one or several genetic mutations transmitted from generation to generation or selected from nondiabetic outbred animals by repeated breeding through several generations. The result is that these animals inherited DM either as single or multigene defects. The metabolic particularities result from single gene defect (monogenic) which is due to dominant gene or recessive gene, or it can be of polygenic

ZDF rats come from a colony of outbred Zucker rats in the laboratory of Dr. Walter Shaw at Eli Lilly Research Laboratories in Indianapolis (USA) during the years 1974–1975. In early 1981, some animals with diabetic lineage were designated and redefined. An inbred line of ZDF rats was established in 1985. Development to a genetic model was established in 1991 [44]. The Zucker fatty (ZF) rats carry a spontaneous mutation in the leptin receptor gene (fa) [45]. ZF rats resulted from the simple autosomal recessive (fa) gene on chromosome 5 [36]. This mutation causes hyperphagia, early onset of obesity, and insulin resistance [14] along with increased growth of subcutaneous fat depot [46]. At the age of 4 weeks, ZF rats gain weight more rapidly due to increased growth of subcutaneous fat depot, and

have special advantages and also disadvantages. The advantages are:

b.Animals develop characteristic features resembling human T2DM.

d.Variability of results is minimal and it required smaller sample size.

b.Limited availability and expensive for the diabetes study.

and requires insulin treatment in later stage for survival.

**78**

origin [36].

they have a noticeably higher body weight at about the age of 9 weeks [47]. The hyperphagia and obesity in ZF rats are attributed to hypothalamic defect in leptin receptor signaling that is related to mild hyperglycemia, mild glucose intolerance, insulin resistance, hyperlipidemia, and moderate hypertension [46]. ZF rats have impaired glucose tolerance rather than apparent diabetes [42].

Thereafter, a mutation in ZF strain led to a substrain with an evident diabetic phenotype—the Zucker diabetic fatty (ZDF) rats [42]. ZDF rats are less obese than ZF rats having a decrease beta cell mass which resulted in inability to compensate for severe insulin resistance [48]. The ZDF rats were derived by selective inbreeding of hyperglycemic ZF rats [49] within the first months of life due to leptin receptor defect and a genetically reduced insulin promoter activity [17]. ZF rats maintain normoglycemia despite their obese phenotype, hyperlipidemia, and hyperinsulinemia [42].

The ZDF male rats became an experimental model for type 2 diabetes mellitus (T2DM). They have a predictable progression from prediabetic to diabetic state [50]. The ZDF rats carry a genetic defect in β-cell transcription. It is inherited independently of the leptin receptor mutation and insulin resistance [17]. In prediabetic stage of ZDF rats, there is no change in insulin mRNA levels. But, significant reduction (30–70%) of other islet mRNA levels, such as glucokinase, mitochondrial glycerol-3-phosphate dehydrogenase, voltage-dependent Ca2+ and K+ channels, Ca2+-ATPase, and transcription factor islet-1 may be detected [51]. It is known that FFA-induced suppression of insulin output in prediabetic stage of ZDF rats is conveyed by nitric oxide (NO) [52]. ZDF rats start to develop T2DM as early as 10 weeks of age, reaching 100% incidence at around 20 weeks of age [53]. It is possible to shorten prediabetic state and reach the symptoms of T2DM after high-energy diet. But, the animals receiving this diet are in the risky group because the diabetic state with its complications arrives quickly and rats can perish. In our experiment with ZDF rats, high-energy diet caused ketoacidosis that meant two cases of animal death in 7th week after initializing feeding with this caloric diet [54].

Blood glucose concentrations in ZDF rats usually increase from 7 to 10 weeks of age and impaired glucose tolerance at 5–7 weeks of age. At the age of 12 weeks, glucose intolerance becomes more severe than at 5–7 weeks of age [55]. Chronic and increasing hyperglycemia in ZDF rats is related to the loss of insulin and pancreatic duodenal homeobox (PDX-1) mRNAs. The lack of glucose stimulated insulin secretion. The possible prevention of hyperglycemia could block the deficit in insulin amount and PDX-1 gene expression and improve insulin secretion [56].

Male ZDF rats that are homozygous recessive have nonfunctional leptin receptors (fa/fa) and develop hyperlipidemia, obesity, and hyperglycemia. Rats that are homozygous dominant (+/+) or heterozygous (fa/+) are lean with normoglycemia. They are healthy, display no symptoms of diabetes, and are usually used as agematch control rats in the experiments. In young fa/fa rats, insulin resistance appears which extends to a deployed insulin secretory defect that initiates hyperglycemia and inadequate β-cell compensation [17, 49]. The insulin resistance is a result of a mutant leptin receptor that causes obesity [17].

In ZDF rats, there are sex differences for phenotypes of diet-induced insulin resistance and glucose intolerance. The most affected are male individuals [57]. On normal diet, male rats from ZDF strain develop severe hypoinsulinemia and hyperglycemia by 4 months of age. Female individuals maintain normal level of blood glucose and insulin despite advanced obesity [38]. Female ZDF rats with fa/fa genotype become also obese and insulin resistant, but do not progress to hyperglycemia, except when fed a high-fat diet [58, 59]. The female

ZDF rats develop T2DM just on a diabetogenic diet [60]. Thus, male ZDF rats are widely used as animal models for human T2DM and diabetic nephropathy and neuropathy [58, 61]. Hyperglycemia in diabetic ZDF rats was recorded at 2.5 month of age, and then blood glucose increased and reached an average value of 29.5 ± 0.9 mM at the age of 5 months. At the age of 5 months, fatty ZDF rats developed significant symptoms of thermal hypoalgesia indicated by prolonged response latencies in a tail-flick test. With progressing diabetes, the markers of thermal hypoalgesia increased at the age of 7 months and persisted till the 10th month [10]. The ZDF rats undergo a rapid transition between 10 and 15 weeks of age. At 10 weeks of age, they are insulin resistant, hyperlipidemic, and hyperinsulinemic. But, the high plasma insulin levels are insufficient to control glucose level, and the animals are hyperglycemic. Between 10 and 15 weeks of age, a loss in insulin secretory function occurs which leads to a marked decline in plasma insulin levels along with hyperglycemia [43]. The ability to secrete insulin to compensate peripheral insulin resistance is limited. β cells of ZDF rats are brittle and easily succumb to over-secretion pressure. The primary defect lies not in the ability of β cells to proliferate but rather in an enhanced rate of apoptosis. It shows impaired insulin secretory β-cell response to glucose, while it remains untouched to non-glucose secretogogues like arginine, a phenomenon similar to human T2DM. Downregulation of β-cell GLUT 2 transporters together with impaired insulin synthesis is probably responsible for hyperglycemia in ZDF animals. Decreased glucose transport activity and lowered GLUT 4 levels are present in the skeletal muscle and adipose tissue [34, 36, 48, 62]. Generally, it was reported that in the progression of ZDF rats, the decline of β-cell glucose transporter 2 (GLUT 2) membrane receptors and the incidental loss of muscle glucose transporter 4 (GLUT 4) are responsible for the impaired insulin secretion and subsequent hyperglycemia. The activity of GLUT 4 receptors decreased in adipose tissue and skeletal muscle. This results in reduced β-cell transport ability together with the peripheral insulin resistance [50].

Siwy et al. [63] characterized the strain of ZDF rats as appropriate model for human disease based on urinary peptidomic profiles. In the study the diabetic rats were heavier than lean individuals. Consistent with a diabetic phenotype, ZDF rats were hyperglycemic and dyslipidemic already at early (2 months of age) and more severely at late (8 month of age). Renal function was markedly impaired at 8 months. Proteinuria was present at 2 months and progressively increased at 8 months. At 8 months, ZDF rats' renal histology showed pathological changes, including glomerular sclerosis with thickening of the Bowman capsule and retraction of the tuft, tubular atrophy and dilatation, and hyaline casts. Lean rats did not develop any histopathological changes. Chen and Wang [44] introduced the following pharmacologically related characteristics of ZDF rats: 25–55% reduction of GLUT 4 in the adipose tissue, heart, and skeletal muscle; loss of pancreatic duodenal homeobox gene expression; and free fatty acids and nitric oxide induced suppression of insulin output (**Table 1**).

Obesity of ZDF rats (fa/fa) is caused by hyperphagia [59], and food restriction can counteract or delay development of T2DM [55]. Hyperphagia leads to hyperinsulinemia, which upregulates transcription factors that stimulate lipogenesis. This results in ectopic deposition of triacylglycerol in non-adipocytes, thereby providing fatty acid substrate for pathological non-oxidative metabolism, such as ceramide synthesis [64].

The severity of DM in the adult hyperglycemic ZDF rats is reflected in body weight and food consumption [42]. High-energy diet in animal's models inclined to DM leads to obesity, hyperinsulinemia, and altered glucose metabolism

**81**

muscle wasting.

patients [66].

*Zucker Diabetic Fatty Rats for Research in Diabetes DOI: http://dx.doi.org/10.5772/intechopen.88161*

T2DM

human type

• Hyperphagia • Polyuria • Polydipsia • Hyperglycemia • Hyperlipidemia • Hyperinsulinemia • Insulin resistance

tissue

Obesity

Genetic feature Leptin receptors

• Associated with obesity

Type of diabetes

Using in research

**Table 1.**

Progression of diabetes

**Main feature Characteristic Description**

Development spontaneously involving

Acceleration of symptoms by high-fat diet Mortality due to ketosis after high-fat diet

Homozygous recessive (fa/fa) rats diabetic homozygous dominant (+/+) and heterozygous (fa/+) remain lean and

Minimal variability of results, the possibility to use small size groups

Predictable progression from prediabetic

genetic factors

Brittle pancreas

normoglycemic

to diabetic state

• Characteristic features resembling

• Reduction of GLUT 4 in adipose

• Genetic defect in β cell transcription

• Defect in leptin signaling

• Insulin receptor deletion

Mechanism of T2DM

Insulin secretory defects Inadequate β cell compensation

*Major genetic, physiological, and pathophysiological characteristics of ZDF rats.*

because of insufficient compensation by the pancreatic islets [31]. In our experiment [54] high-energy diet immediately induced hyperglycemia in ZDF rats, animals developed obesity, and we observed disturbance in some hematology parameters as neutrophils, mean platelet volume (MPV), and platelet count (PLT), which is a possible marker of angiopathy. In the groups of diabetic rats, we observed the significant weight decrease when compared to the control animals. It is probably linked to accelerated switch from prediabetic to diabetic state. It suggests the inability to utilize the calories consumed [42] and the degradation of structural proteins and muscle wasting in diabetic individuals [65]. Hempe et al. [59] found that body weight of ZDF obese rats was higher than the lean rats at the beginning of their study. Later, at around 16 weeks of age, body weight of obese animals started to decline. Lean rats reached the same body weight as obese rats at 25 weeks of age. The decrease of weight in obese diabetic rats on high energy is linked to accelerated switch from prediabetic to diabetic accomplished with associated complications of T2DM. Oyedemi et al. [65] explained this reduction in body weight as degradation of structural proteins and

Hempe et al. [59] evaluated if nephropathy and neuropathy in ZDF rats are linked to the hyperglycemic state of the rats and are real diabetic late complications or are related to other characteristics of the fa/fa genotype. Good glycemic control may be effective in delaying the neuropathic symptoms in diabetic

*Zucker Diabetic Fatty Rats for Research in Diabetes DOI: http://dx.doi.org/10.5772/intechopen.88161*

#### **Table 1.**

*Animal Models in Medicine and Biology*

with the peripheral insulin resistance [50].

suppression of insulin output (**Table 1**).

ZDF rats develop T2DM just on a diabetogenic diet [60]. Thus, male ZDF rats are widely used as animal models for human T2DM and diabetic nephropathy and neuropathy [58, 61]. Hyperglycemia in diabetic ZDF rats was recorded at 2.5 month of age, and then blood glucose increased and reached an average value of 29.5 ± 0.9 mM at the age of 5 months. At the age of 5 months, fatty ZDF rats developed significant symptoms of thermal hypoalgesia indicated by prolonged response latencies in a tail-flick test. With progressing diabetes, the markers of thermal hypoalgesia increased at the age of 7 months and persisted till the 10th month [10]. The ZDF rats undergo a rapid transition between 10 and 15 weeks of age. At 10 weeks of age, they are insulin resistant, hyperlipidemic, and hyperinsulinemic. But, the high plasma insulin levels are insufficient to control glucose level, and the animals are hyperglycemic. Between 10 and 15 weeks of age, a loss in insulin secretory function occurs which leads to a marked decline in plasma insulin levels along with hyperglycemia [43]. The ability to secrete insulin to compensate peripheral insulin resistance is limited. β cells of ZDF rats are brittle and easily succumb to over-secretion pressure. The primary defect lies not in the ability of β cells to proliferate but rather in an enhanced rate of apoptosis. It shows impaired insulin secretory β-cell response to glucose, while it remains untouched to non-glucose secretogogues like arginine, a phenomenon similar to human T2DM. Downregulation of β-cell GLUT 2 transporters together with impaired insulin synthesis is probably responsible for hyperglycemia in ZDF animals. Decreased glucose transport activity and lowered GLUT 4 levels are present in the skeletal muscle and adipose tissue [34, 36, 48, 62]. Generally, it was reported that in the progression of ZDF rats, the decline of β-cell glucose transporter 2 (GLUT 2) membrane receptors and the incidental loss of muscle glucose transporter 4 (GLUT 4) are responsible for the impaired insulin secretion and subsequent hyperglycemia. The activity of GLUT 4 receptors decreased in adipose tissue and skeletal muscle. This results in reduced β-cell transport ability together

Siwy et al. [63] characterized the strain of ZDF rats as appropriate model for human disease based on urinary peptidomic profiles. In the study the diabetic rats were heavier than lean individuals. Consistent with a diabetic phenotype, ZDF rats were hyperglycemic and dyslipidemic already at early (2 months of age) and more severely at late (8 month of age). Renal function was markedly impaired at 8 months. Proteinuria was present at 2 months and progressively increased at 8 months. At 8 months, ZDF rats' renal histology showed pathological changes, including glomerular sclerosis with thickening of the Bowman capsule and retraction of the tuft, tubular atrophy and dilatation, and hyaline casts. Lean rats did not develop any histopathological changes. Chen and Wang [44] introduced the following pharmacologically related characteristics of ZDF rats: 25–55% reduction of GLUT 4 in the adipose tissue, heart, and skeletal muscle; loss of pancreatic duodenal homeobox gene expression; and free fatty acids and nitric oxide induced

Obesity of ZDF rats (fa/fa) is caused by hyperphagia [59], and food restriction can counteract or delay development of T2DM [55]. Hyperphagia leads to hyperinsulinemia, which upregulates transcription factors that stimulate lipogenesis. This results in ectopic deposition of triacylglycerol in non-adipocytes, thereby providing fatty acid substrate for pathological non-oxidative metabolism, such as ceramide

The severity of DM in the adult hyperglycemic ZDF rats is reflected in body weight and food consumption [42]. High-energy diet in animal's models inclined to DM leads to obesity, hyperinsulinemia, and altered glucose metabolism

**80**

synthesis [64].

*Major genetic, physiological, and pathophysiological characteristics of ZDF rats.*

because of insufficient compensation by the pancreatic islets [31]. In our experiment [54] high-energy diet immediately induced hyperglycemia in ZDF rats, animals developed obesity, and we observed disturbance in some hematology parameters as neutrophils, mean platelet volume (MPV), and platelet count (PLT), which is a possible marker of angiopathy. In the groups of diabetic rats, we observed the significant weight decrease when compared to the control animals. It is probably linked to accelerated switch from prediabetic to diabetic state. It suggests the inability to utilize the calories consumed [42] and the degradation of structural proteins and muscle wasting in diabetic individuals [65]. Hempe et al. [59] found that body weight of ZDF obese rats was higher than the lean rats at the beginning of their study. Later, at around 16 weeks of age, body weight of obese animals started to decline. Lean rats reached the same body weight as obese rats at 25 weeks of age. The decrease of weight in obese diabetic rats on high energy is linked to accelerated switch from prediabetic to diabetic accomplished with associated complications of T2DM. Oyedemi et al. [65] explained this reduction in body weight as degradation of structural proteins and muscle wasting.

Hempe et al. [59] evaluated if nephropathy and neuropathy in ZDF rats are linked to the hyperglycemic state of the rats and are real diabetic late complications or are related to other characteristics of the fa/fa genotype. Good glycemic control may be effective in delaying the neuropathic symptoms in diabetic patients [66].


**4. Materials and Methods**

#### *4.1. Materials*

The wild-type strain *S. cerevisiae* BY4742 (ATCC®, 201389TM) (*MAT*α *his3*Δ1 *leu2*Δ0 *lys2*Δ0 *ura3*Δ0) was obtained from American Type Culture Collection (Manassas, VA, USA). The culture of yeast reference strain was aliquoted into 10 μL and stored at −80 ◦C. All L-amino acids, yeast nitrogen base w/o amino acids (YNB), ammonium sulfate, peptone, agar and yeast extract, H2DCFDA, 2,4,6-tripyridyl-s-triazine (TPTZ), 2,2- -azino-bis (3-ethylbenzothiazoline-6-sulfonic acid) (ABTS), 1,1-diphenyl-2-picrylhydrazyl (DPPH), dimethyl sulfoxide (DMSO), neohesperidin, naringin, hesperidin and hesperetin were bought from Sigma-Aldrich (Shanghai, China). YPD Broth, YPD and other chemicals were from Solebo biotech Co., Ltd. (Beijing, China). The 96-well polystyrene microplates with flat bottom were purchased from Corning incorporated (Kennebunk, ME, USA).

#### *4.2. Lifespan and Yeast Cell Growth Assay*

The determination of chronological lifespan (CLS) of yeast was carried out according to the method of Wu et al. [25] with a moderate modification as follows. In brief, the yeast cells were prepared by transferring a streaked strain from frozen stocks onto YPD agar (0.5% yeast extract/1% peptone/2% dextrose/1.4% agar) plates. After incubating the cells at 30 ◦C for 2 days, a single colony was picked and inoculated into a 1.0-mL YPD liquid medium (1% yeast extract/2% peptone/2% dextrose) in a 10-mL sterilized centrifuge tube (round bottom) and cultured at 30 ◦C for 2 days in a flat incubator at 200 rpm. The 2-day YPD culture was diluted with autoclaved 18 mΩ Milli-Q grade water (1:10) and stored in a refrigerator at 4 ◦C for 2 days. After 2-day incubation at 4 ◦C, 5 μL (≈ 1 × 104 cells) of the diluted culture was transferred to 993 microliter of synthetic-defined (SD) media (Supplementary Table S1, [51]) and maintained at 30 ◦C, 200 rpm for the entire experiment. Compounds in DMSO with several concentrations (2.0 μL) were added at the initial inoculation (0 h). Each experiment was performed at least in triplicate. Cell cultures were incubated at 30 ◦C without replacing the aging medium throughout the experiment. After 2 days of culture in an aging media, the cells reached stationary phase and the first age-point was then taken. Subsequent age-points were taken every 2–4 days. For each age point, 5.0 μL of the mixed culture was pipetted into each well of 96-well flat-bottom microplate. Ninety-five microliter YPD medium was then added to each well. The cell population was monitored with a microplate reader (Varioskan Flash; Thermo Scientific, Waltham, MA, USA) by recording OD660 every 10 min during 24 h.

The survival rate was calculated as follows [25]. Where tOD= 0.3, 2day is the time that OD value of day 2 age-point reaches 0.3 in the outgrowth curves. The initial age-point (day 2) is defined to be 100% viability and the relative survival percent of each successive age-point can be calculated as follows:

$$Vn = \frac{1}{2\frac{\Delta t\_n}{Dt\_n}} \times 100n = days.\ \overline{Dt\_n}\text{ represent the average doubling time.}$$

The survival integral (SI) for each well is defined as the area under the survival curve (AUC) and can be estimated by the formula:

$$\text{SI} = \sum\_{2}^{n} \left( \frac{V\_{n-1} + V\_n}{2} \right) \left( day\_n - day\_{n-1} \right)$$

where *dayn* is the age point, such as days 2, 4, 6, 8, 10, 12, 14, 16, 18 and 20.

#### *4.3. Intracellular ROS Scavenging Ability Assays*

To quantify the intracellular reactive oxygen species (ROS) level of yeast cells grown in standard SD medium with/without the four compounds, the method described in Wu et al. [51] had been referenced. Namely, 2 μL ROS probe H2DCFDA from a fresh 5-mM stock solution in DMSO was added into 1.0 mL yeast aging culture (at day 2) at 30 ◦C for 1 h. The culture was then washed twice in sterile distilled water and suspended in 1.0 mL of 50 mM Tris/Cl buffer (pH 7.5). Twenty microliter of chloroform and 10 μL of 0.1% (*w*/*v*) sodium dodecyl sulfate (SDS) were added, and the cells were incubated at 200 rpm for 30 min to allow the dye to diffuse. The culture was centrifuged at 5000 rpm for 5 min, and the fluorescence of the supernatant was measured using a microplate reader with excitation at 480 nm and emission at 520 nm.

#### *4.4. Antioxidant Activity Assays*

In this study, DPPH, FRAP and ABTS assays were used for in vitro antioxidant capacity evaluation. The DPPH assay was performed according to the method described by Barreca et al. [53]. An aliquot of each sample (0.5 mL) was mixed with 75 μM (3.5 mL) of DPPH in methanol to a final volume of 4.0 mL. After reacting for 30 min without light, the absorption of the mixture was detected at a wavelength of 517 nm. The inhibition percentage of radical scavenging activity was the DPPH value. The FRAP assay was carried out according to Hungder et al. [54] with some modifications. A 0.2 mL aliquot of the sample was mixed with 3.8 mL of FRAP reagent (0.3 mol/L acetate buffer (pH 3.6), 10 mmol/L TPTZ solution, and 20 mmol/L ferric chloride (FeCl3) were mixed (10:1:1, volume ratio)). After 30 min, the absorbance was detected at wavelength of 593 nm. And the ABTS assay was followed the method of Mnb et al. [55] with few modifications. The ABTS radical cation (ABTS •+) was generated by reaction of 176 μL of potassium persulfate solution (140 mM) and 10 mL aqueous ABTS solution (7 mM) under the condition of no light for 12–16 h. Then it was diluted with methanol to an absorption value of 0.7 ± 0.02 units at 734 nm. 0.1 mL sample was added to 4.9 mL ABTS reagent. The absorbance was measured at a wavelength of 734 nm after 10 min reaction. All absorbance values were determined by using the UV–VIS spectrophotometer (PerkinElmer Lambda 25 UV/VIS, Waltham, MA, USA). Antioxidant values were calculated by standard curve method and expressed as trolox equivalents (TE mg/g DW).

### *4.5. Extracellular pH Detection*

The culture process of yeast in the early stage was almost the same as the method described in the part of "Lifespan and yeast cell growth assay". The specific operation was as follows. The yeast cells were prepared by transferring the yeast strain from frozen stocks onto YPD agar plates. After incubating the cells at 30 ◦C for 2 days, a single colony was picked and inoculated into a 1.0-mL YPD liquid medium in a 10-mL sterilized centrifuge tube and cultured at 30 ◦C for 2 days in a flat incubator at 200 rpm. The 2-day YPD culture was diluted with autoclaved 18 mΩ Milli-Q grade water (1:10) and stored in a refrigerator at 4 ◦C for 2 days. After 2-day incubation at 4 ◦C, 10 μL (≈ 2 × 104 cells) of the diluted culture was transferred to 1986 μL of SD media and maintained at 30 ◦C, 200 rpm for 2/10/20 days. Various compounds in DMSO (4.0 μL) were add to the medium to a final concentration of 10 μM at initial inoculation (0 h). Then 1mL of the 2/10/20-day SD culture was added to 19 mL fresh YPD liquid medium. The pH was tested every five minutes using a pH meter while the yeast was cultured at 30 ◦C in a shaker at 200 rpm for the whole detection. Each experiment was performed at least in triplicate.


**3.1 Weight reduction**

Lifestyle modification is the recommended first step in the treatment of GERD. However, the only measures that have been shown to be beneficial on the part of obese patient is weight loss [37]. Weight loss is strongly recommended in overweight or obese GERD patients to improve the reflux symptoms [6, 36]. A prospective cohort study has found that in GERD subjects with overweight and obesity, weight reduction was significantly decreased the overall prevalence of GERD with significant improvement in overall symptoms scoring, compared to baseline [38]. The result of this study also showed a substantial reduction in overall GERD scores only observed among subjects who loss body weight ≥5% from baseline. Study conducted by de Bortoli *et al*. found that group of GERD patients who had weight reduction was showing not only a higher rate of symptoms improvement, but also managed to reduce the dosage of proton pump inhibitor (PPI), compared to group without weight reduction [39].

*Gastroesophageal Reflux Disease and Obesity DOI: http://dx.doi.org/10.5772/intechopen.106528*

This study also recommend all patients with GERD to achieve a minimum 10% weight loss from baseline in order to hasten the efficacy of PPI to relieve GERD symptom [39]. The result of the above studies is supported by the finding of dose-dependent relationship between reduction in body weight and improvement of GERD symptoms [40]. Study conducted by Park *et al* found weight reduction was significantly associated with improvement of GERD symptom, but showed no association with improvement in erosive esophagitis [41].


**5. Conclusion and suggestion**

In order to achieve high precision and yield, modern FABs use a large number of high-energy processes such as plasma, CVD and ion implantation, the furnace is one of the important tools of semiconductor manufacturing. The FAB installed FTIR system due to the 12″ furnace tools based on the aforementioned production management requirements. The principle of measurement is the same as the principle of Extractive FTIR, but the closed cavity is changed to open type and integrated IoT mechanism to connect to the cloud, which is suitable for a variety of gaseous pollutants (including organic gases and inorganic gaseous pollutants) in the atmosphere are monitored in this study. This study set up two measuring points of furnace process tools in the 12″ factory of Hsinchu Science Park in Taiwan. This study obtained FTIR measurements, and according to the OHSA regulations, this study is set in the cloud database for big data analysis and decision making, when the upper limit of TEOS, C2H4, CO are 0.6, 2.0, 1.7 ppm; the lower limit of TEOS, C2H4, CO is 0.4 , 1.5, 1 ppm. The application architecture of this study can be extended to other semiconductor processes, so that IoT integration and big data operations can be performed for all processes, this is an important step in promoting FAB intelligent production and an important contribution of this study.

**Author details**

Technology, Taiwan

University, Taiwan

**95**

Kuo-Chi Chang1,2\*, Kai-Chun Chu1

Tsui-Lien Hsu4 and Yu-Wen Zhou1

1 Fujian University of Technology, China

*DOI: http://dx.doi.org/10.5772/intechopen.92849*

provided the original work is properly cited.

, Hsiao-Chuan Wang3

2 College of Mechanical and Electrical Engineering, National Taipei University of

*Study on IoT and Big Data Analysis of 12" 7 nm Advanced Furnace Process Exhaust Gas Leakage*

3 Institute of Environmental Engineering, National Taiwan University, Taiwan

© 2020 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium,

4 Institute of Construction Engineering and Management, National Central

\*Address all correspondence to<EMAIL_ADDRESS>
, Yuh-Chung Lin1

,

*Study on IoT and Big Data Analysis of 12" 7 nm Advanced Furnace Process Exhaust Gas Leakage DOI: http://dx.doi.org/10.5772/intechopen.92849*


5. Derivation of the initial equations

Let us turn further to the longitudinal oscillations.

The interaction of the elastic wave is largely with the interface of the media due to the wave impedance, which is determined by the relation [34]. It follows that

$$-\frac{\sigma}{\nu} = \rho a\_1,\tag{33}$$

where a1 is the velocity of propagation of longitudinal oscillations in the medium.

When considering harmonic oscillations propagating along a line, we usually study the wave resistance in operator form or mechanical impedance

$$Z\_b(j\rho) = \frac{\sigma(j\rho)}{\nu(j\rho)}.\tag{34}$$

Referring to Formula (34) and taking into account that

$$a\_1 = \Theta \sqrt{\frac{E}{\rho}},\tag{35}$$

where [34]

$$\Theta = \sqrt{\frac{1-\mu}{(1+\mu)(1-2\mu)}},\tag{36}$$

we write

$$Z\_b(\
ja) = \rho(o)\Theta\sqrt{\frac{E\_o(\
ja)}{\rho(\
ja)}} = \Theta\sqrt{E\_o(\
ja)\rho(\
ja)}.\tag{37}$$

we obtain

The solution is

Let at x = 0

ρsυðÞ¼� s

E dυð Þs

Dynamic Stability of Open Two-Link Mechanical Structures

DOI: http://dx.doi.org/10.5772/intechopen.91045

the line, depend on the physical and geometric properties of the line.

dυ(s)/dx using Eq. (24), and applying relation (20), we obtain

∂2 σð Þs ∂x2 � θ2

σð Þ¼ s, x σ1ð Þ s, 0 ;

�1θð Þs Eυ1ð Þ s, 0

After substituting these dependencies, the solution will be

When we introduce hyperbolic functions, then we get

σð Þ¼ s, x σ1ð Þ s, 0 ch½ �� θð Þs x θð Þs s

∂2 υð Þs ∂x2 � θ2

Then, taking into account (49), we get

� s

C1 ¼ σ1ð Þ� s, 0 s

manner described, we obtain

13

σð Þ¼ s, x

Differentiating Eq. (23) with respect to x, then eliminating the derivative

This equation is a second-order differential equation with constant coefficients.

The integration constants C1 and C2 are determined by the boundary conditions.

∂x ¼ � E

∂σð Þ s, x

The last condition from (49) is obtained from (45) by replacing ρs = θ2

2 ; С2 ¼ σ1ð Þþ s, 0 s

σ1ð Þ s, 0 f g exp ½ �þ θð Þs x exp ½ � �θð Þs x 2

Having solved the system of Eqs. (47) and (48) with respect to υ(s, x) in the

�1θð Þs Eσ1ð Þ s, 0 f g exp ½ �� θð Þs x exp ½ � �θð Þs x

�1

σðÞ¼ s C1 exp ½ �þ θð Þs x C2 exp ½ � �θð Þs : (48)

s θ2

dσð Þs

The solution of the system of Eqs. (45) and (46) allows to find for the selected section the instantaneous deviations from the steady-state values of stress and speed of movement sections of rod. Each of these quantities will be the sum of the quantities of the same name, determined in the front of the perturbation propagating in the forward and reverse directions. The instantaneous deviations of the marked variables, as well as the peculiarities of the disturbance propagation along

dx ; (45)

dx ¼ �sσð Þs : (46)

ð Þs σðÞ¼ s 0: (47)

ð Þs υ1ð Þ s, 0 : (49)

2 : (50)

�1θð Þs Eυ1ð Þ s, 0

2 : (51)

Eυ1ð Þ s, 0 sh½ � θð Þs x : (52)

ð Þs υðÞ¼ s 0: (53)

(s)Е/s.

Note that the ratio Eυ/Eu = tg ξ characterizes the magnitude of internal friction and ξ determines the phase on which the change of stress is ahead of the change in deformation.

Then Eq. (37) becomes

$$Z\_b(\ j a) = \frac{\sigma(\ j a)}{\nu(\ j a)} = \Theta \sqrt{E\_u(o)\rho(o)} \sqrt{\mathbf{1} + j \frac{E\_v(o)}{E\_u(o)}}.\tag{38}$$

If ρ = const and Θ = 1, then the last equation may be written in the form

$$Z\_b(j\omega) = \frac{j\alpha \mathcal{E}\_u(\alpha)\sqrt{\mathfrak{p}/\mathcal{E}\_u(\alpha)}\sqrt{\mathfrak{1} + j\mathcal{E}\_v(\alpha)/\mathcal{E}\_u(\alpha)}}{j\alpha} = \frac{\mathcal{E}\_u(\alpha)\mathfrak{d}(j\omega)}{j\alpha}.\tag{39}$$

Here

$$\Theta(j\rho) = \pm \sqrt{j \frac{\alpha}{E\_u(\rho)} [\rho j \rho + \wp(\rho)]}; \ \wp(\rho) = -\frac{\rho \alpha E\_v(\rho)}{E\_u(\rho)}. \tag{40}$$

Internal friction in solids ψ can play a significant role. For example, it is known that magnesium alloys and a number of other materials have very good vibrationinsulating properties, largely due to internal friction. At the same time, for steels this value is small and it is often neglected.

The dynamic features of lines with parameters distributed over length (in principle, parameters are distributed in any line) are characterized by the operator coefficient of wave propagation, which, in Laplace images, can be written in the form [29, 31]

$$\Theta(s) = \pm \sqrt{\frac{s}{E\_u(o)} [\rho s + \varphi(o)]}.\tag{41}$$

Then, when Eυ = 0, ρ = const, and Eu = E, the wave resistance will be

$$Z\_b(\mathfrak{s}) = \frac{\sigma(\mathfrak{s})}{\nu(\mathfrak{s})} = \frac{\theta(\mathfrak{s})E}{\mathfrak{s}}.\tag{42}$$

From where it also follows

$$
\theta(\mathfrak{s}) = \frac{sZ\_b(\mathfrak{s})}{E}.\tag{43}
$$

Conducting a one-dimensional Laplace transform [30] of Eqs. (13) and (14) for longitudinal oscillations with zero initial conditions and taking into account that with the accepted assumptions

$$
\Theta(\mathfrak{s}) = \pm \mathfrak{s} \sqrt{\frac{\mathfrak{p}}{E}} \tag{44}
$$

Dynamic Stability of Open Two-Link Mechanical Structures DOI: http://dx.doi.org/10.5772/intechopen.91045

we obtain

we write

deformation.

Here

form [29, 31]

Then Eq. (37) becomes

Zbð Þ¼ jω ρð Þ ω Θ

Truss and Frames - Recent Advances and New Perspectives

Zbð Þ¼ jω σð Þ jω

Zbð Þ¼ jω jωEuð Þ ω ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

θð Þ¼� jω

this value is small and it is often neglected.

From where it also follows

with the accepted assumptions

12

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Eωð Þ jω ρð Þ jω

Note that the ratio Eυ/Eu = tg ξ characterizes the magnitude of internal friction and ξ determines the phase on which the change of stress is ahead of the change in

υð Þ jω ¼ Θ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

If ρ = const and Θ = 1, then the last equation may be written in the form

ρ=Euð Þ ω p ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

Euð Þ ω ½ � ρjω þ ψ ωð Þ

Internal friction in solids ψ can play a significant role. For example, it is known that magnesium alloys and a number of other materials have very good vibrationinsulating properties, largely due to internal friction. At the same time, for steels

> ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi s Euð Þ ω ½ � ρs þ ψ ωð Þ

The dynamic features of lines with parameters distributed over length (in principle, parameters are distributed in any line) are characterized by the operator coefficient of wave propagation, which, in Laplace images, can be written in the

r

Then, when Eυ = 0, ρ = const, and Eu = E, the wave resistance will be

θðÞ¼ s

θðÞ¼� s s

σð Þs υð Þs ¼ θð Þs E

sZbð Þs

Conducting a one-dimensional Laplace transform [30] of Eqs. (13) and (14) for longitudinal oscillations with zero initial conditions and taking into account that

> ffiffiffi ρ E r

ZbðÞ¼ s

j ω

θðÞ¼� s

r

1 þ jEυð Þ ω =Euð Þ ω p

¼ Θ

q

Euð Þ ω ρð Þ ω p ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 þ j

jω ¼ Euð Þ ω θð Þ jω

; ψ ωð Þ¼� ρωEυð Þ ω

s

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Eωð Þ jω ρð Þ jω

> Eυð Þ ω Euð Þ ω

: (37)

: (38)

jω : (39)

Euð Þ ω : (40)

: (41)

s : (42)

E : (43)

, (44)

s

$$
\rho \mathfrak{so}(\mathfrak{s}) = -\frac{d\sigma(\mathfrak{s})}{d\mathfrak{x}};\tag{45}
$$

$$E\frac{d\nu(s)}{d\kappa} = -s\sigma(s). \tag{46}$$

The solution of the system of Eqs. (45) and (46) allows to find for the selected section the instantaneous deviations from the steady-state values of stress and speed of movement sections of rod. Each of these quantities will be the sum of the quantities of the same name, determined in the front of the perturbation propagating in the forward and reverse directions. The instantaneous deviations of the marked variables, as well as the peculiarities of the disturbance propagation along the line, depend on the physical and geometric properties of the line.

Differentiating Eq. (23) with respect to x, then eliminating the derivative dυ(s)/dx using Eq. (24), and applying relation (20), we obtain

$$\frac{\partial^2 \sigma(s)}{\partial \mathbf{x}^2} - \theta^2(s)\sigma(s) = \mathbf{0}.\tag{47}$$

This equation is a second-order differential equation with constant coefficients. The solution is

$$
\sigma(\mathfrak{s}) = \mathbf{C}\_1 \exp\left[\theta(\mathfrak{s})\mathfrak{x}\right] + \mathbf{C}\_2 \exp\left[-\theta(\mathfrak{s})\right].\tag{48}
$$

The integration constants C1 and C2 are determined by the boundary conditions. Let at x = 0

$$
\sigma(\mathfrak{s}, \mathfrak{x}) = \sigma\_1(\mathfrak{s}, \mathbf{0}); \frac{\partial \sigma(\mathfrak{s}, \mathfrak{x})}{\partial \mathfrak{x}} = -\frac{E}{\mathfrak{s}} \Theta^2(\mathfrak{s}) \nu\_1(\mathfrak{s}, \mathbf{0}).\tag{49}
$$

The last condition from (49) is obtained from (45) by replacing ρs = θ2 (s)Е/s. Then, taking into account (49), we get

$$C\_1 = \frac{\sigma\_1(\mathfrak{s}, \mathfrak{0}) - \mathfrak{s}^{-1}\theta(\mathfrak{s})E\nu\_1(\mathfrak{s}, \mathfrak{0})}{2};\\C\_2 = \frac{\sigma\_1(\mathfrak{s}, \mathfrak{0}) + \mathfrak{s}^{-1}\theta(\mathfrak{s})E\nu\_1(\mathfrak{s}, \mathfrak{0})}{2}.\tag{50}$$

After substituting these dependencies, the solution will be

$$\sigma(s,\mathbf{x}) = \frac{\sigma\_1(s,\mathbf{0})\{\exp\left[\theta(s)\mathbf{x}\right] + \exp\left[-\theta(s)\mathbf{x}\right]\}}{-\frac{s^{-1}\theta(s)E\sigma\_1(s,\mathbf{0})\{\exp\left[\theta(s)\mathbf{x}\right] - \exp\left[-\theta(s)\mathbf{x}\right]\}}{2}}.\tag{51}$$

When we introduce hyperbolic functions, then we get

$$
\sigma(\boldsymbol{\varsigma}, \boldsymbol{\varsigma}) = \sigma\_1(\boldsymbol{\varsigma}, \mathbf{0}) ch[\boldsymbol{\Theta}(\boldsymbol{\varsigma})\boldsymbol{\varkappa}] - \boldsymbol{\Theta}(\boldsymbol{\varsigma}) \boldsymbol{\varsigma}^{-1} E \nu\_1(\boldsymbol{\varsigma}, \mathbf{0}) sh[\boldsymbol{\Theta}(\boldsymbol{\varsigma})\boldsymbol{\varkappa}].\tag{52}
$$

Having solved the system of Eqs. (47) and (48) with respect to υ(s, x) in the manner described, we obtain

$$\frac{\partial^2 \nu(s)}{\partial \mathbf{x}^2} - \Theta^2(s)\nu(s) = \mathbf{0}.\tag{53}$$

For boundary conditions with x = 0

$$\nu(\mathfrak{s}, \mathfrak{x}) = \nu\_1(\mathfrak{s}, \mathbf{0}); \frac{\partial \nu(\mathfrak{s}, \mathfrak{x})}{\partial \mathfrak{x}} = -\frac{\mathfrak{s}\sigma(\mathfrak{s}, \mathbf{0})}{E},\tag{54}$$

σ2ðÞ¼ s

Dynamic Stability of Open Two-Link Mechanical Structures

DOI: http://dx.doi.org/10.5772/intechopen.91045

Ω2ð Þs 1 þ hkϑkð Þs s þ Jϑkð Þs s

GrWp2

analyzing the operation of the hydraulic drive [9, 35–37].

Here

influence of F on σ:

WFð Þ¼ jω υ2ð Þ jω

WFσð Þ¼ jω σ2ð Þ jω

Wυð Þ¼ jω υ2ð Þ jω

We introduce the notation α = l ω (ρ/E)

Znð Þ¼ jω th½ � θð Þ jω l

WFσð Þ¼ jω σ2ð Þ jω

Insofar as

then

15

ϑkðÞ¼ s ϑk0Zkð Þs ; ϑk0 ¼ l

FcðÞþs υ1ð Þs ð Þ hn þ ms =chA

chAk

Performing such transformations in relation to torsional vibrations, we obtain

thAk Ak

Comparing (15), (18), and (19), we can see that the processes of motion transfer in solid and liquid media can be described by similar equations. This is shown when

Eqs. (47) and (48) make it possible to calculate the frequency characteristics of the system, i.e., determine the response of the model to the harmonic change in the

For F � 0, we obtain the frequency characteristics Wυ (jω), illustrating the effect

2 � � ¼ Ω1ð Þs

; ZkðÞ¼ s

6. Lemma on the degree of distribution of force line parameters

speed of the lead link or the resistance force acting on the driven link.

For example, for υ1 � 0 and s=jω, we obtain the characteristic WF (jω), illustrating the influence of F on υ2, and the characteristic WFσ (jω), illustrating the

Fcð Þ jω ¼ � ϑnð Þ jω jω

of υ1 on υ2, and WFσ (jω), illustrating the influence of υ1 on σ2. So we have

Fcð Þ jω ¼ 1

υ1ð Þ jω ¼ � сh�1

υ1ð Þ jω ¼ hn þ mjω

θð Þ jω l ¼ jtgα

From (63) to (66), it can be seen that changes in the voltage and speed of movement of the output link are lagging behind changes in input impacts.

1/2.

jα ¼ tgα

f 2 1 þ hnϑnð Þs s þ mϑnð Þs s2 ½ � : (60)

; Ak ¼ θkð Þs l; θkðÞ¼� s

1 þ hnϑnð Þ jω jω þ mϑnð Þ jω ð Þ jω 2 ; (63)

f 2 1 þ hnϑnð Þ jω jω þ mϑnð Þ jω ð Þ jω 2 h i : (64)

1 þ hnϑnð Þ jω jω þ mϑnð Þ jω ð Þ jω 2 , (65)

α ; ch j ð Þ¼ α cos α, (67)

½ � θð Þ jω l

f 2ch½ � θð Þ jω l 1 þ hnϑnð Þ jω jω þ mϑnð Þ jω ð Þ jω 2 h i : (66)

� Mrð Þs ϑnð Þs s: (61)

ffiffiffiffi ρ G r

: (62)

We finally obtain

$$\nu(\mathfrak{s}, \mathfrak{x}) = \nu\_1(\mathfrak{s}, \mathfrak{O}) ch[\mathfrak{G}(\mathfrak{s})\mathfrak{x}] - \frac{s \sigma\_1(\mathfrak{s}, \mathfrak{O}) ch[\mathfrak{G}(\mathfrak{s})\mathfrak{x}]}{\mathfrak{G}(\mathfrak{s}) E} \,. \tag{55}$$

Movement in two-link elements that occurs within elastic limits can be viewed as the movement of the driven point (link) from the movement of the leading point (link), which is affected by the previous links of the truss, for example, which perceive wind load. If, in the process of oscillation, the output link does not allow the input impulse to pass, then waves of disturbance are reflected from the end of the lines.

Consider the case of a matched load when there are no reflected waves in the system and oscillations in the system do not affect the movement of the driven link due to the attached large mass. In this case, the boundary conditions are the following relations:

$$\begin{aligned} \nu(s,l) &= \nu\_2(s); \ \nu(s,0) = \nu\_1(s); \ \sigma(s,l) = \sigma\_2(s); \ \sigma(s,0) = \sigma\_1(s);\\ \sigma\_2(s) &= \frac{F\_\varepsilon(s) + h\_n \nu\_2(s) + ms \nu\_2(s)}{f\_2}. \end{aligned} \tag{56}$$

Here f2 is the sectional area of the line in front of the slave link of mass m; hn and Fс are coefficient of friction loss, proportional to the speed of movement, as well as the resistance force acting on the slave link; l is the length of the line.

Together we solve (52)–(56) by performing the following transformations

$$\begin{aligned} \sigma\_1(s) &= \frac{1}{chA} \left[ \sigma\_2(s) + \frac{1}{s} E \nu\_1(s) \theta(s) hA \right]; \\ \nu\_2(s) &= \nu\_1(s) chA - \frac{s}{E\theta(s)} shA \left\{ \frac{1}{chA} \left[ \sigma\_2(s) + \frac{1}{s} E \nu\_1(s) \theta(s) shA \right] \right\}; \\ \nu\_2(s) &= \frac{\nu\_1(s)}{chA} - \frac{s}{E\theta(s)} \sigma\_2(s) thA; \\ \left[ \frac{\nu\_1(s)}{chA} - \nu\_2(s) \right] \frac{E}{s} \frac{\theta(s)}{thA} &= \frac{1}{f\_2} [F(s) + h\_n \nu\_2(s) + m \nu\_2(s)]. \end{aligned} \tag{57}$$

After bringing similar members, we obtain the equation of motion of the driven link of the mechanical system in the form

$$
\eta\_2(\boldsymbol{\varsigma}) \left[ \mathbf{1} + h\_n \theta\_n(\boldsymbol{\varsigma}) \boldsymbol{\varsigma} + m \theta\_n(\boldsymbol{\varsigma}) \boldsymbol{\varsigma}^2 \right] = \frac{\nu\_1(\boldsymbol{\varsigma})}{ch[\boldsymbol{\Theta}(\boldsymbol{\varsigma}) \boldsymbol{l}]} - F\_c(\boldsymbol{\varsigma}) \theta\_n(\boldsymbol{\varsigma}) \boldsymbol{\varsigma}. \tag{58}
$$

Here

$$\theta\_n(s) = \theta\_{n0} Z\_n(s); \theta\_{n0} = \frac{l}{Ef\_2}; Z\_n(s) = \frac{thA}{A}; A = \theta(s)l. \tag{59}$$

Substituting (58) into the last equation of system (57), we obtain an equation describing the stresses fluctuations in the force line in the vicinity of the slave link in form

Dynamic Stability of Open Two-Link Mechanical Structures DOI: http://dx.doi.org/10.5772/intechopen.91045

$$\sigma\_2(s) = \frac{F\_c(s) + \nu\_1(s)(h\_n + ms)/chA}{f\_2[1 + h\_n\theta\_n(s)s + m\theta\_n(s)s^2]}.\tag{60}$$

Performing such transformations in relation to torsional vibrations, we obtain

$$\mathfrak{Q}\_2(\mathfrak{s}) \left[ \mathbf{1} + h\_k \mathfrak{G}\_k(\mathfrak{s}) \mathfrak{s} + J \mathfrak{G}\_k(\mathfrak{s}) \mathfrak{s}^2 \right] = \frac{\mathfrak{Q}\_1(\mathfrak{s})}{chA\_k} - M\_r(\mathfrak{s}) \mathfrak{G}\_n(\mathfrak{s}) \mathfrak{s}. \tag{61}$$

Here

For boundary conditions with x = 0

Truss and Frames - Recent Advances and New Perspectives

We finally obtain

lowing relations:

σ2ðÞ¼ s

σ1ðÞ¼ s

υ1ð Þs chA � υ2ð Þs E

Here

in form

14

υ2ðÞ¼ s υ1ð Þs

1

υ2ðÞ¼ s υ1ð Þs chA � s

chA � s

Eθð Þs

s θð Þs thA ¼ 1 f 2

driven link of the mechanical system in the form

υ2ð Þs 1 þ hnϑnð Þs s þ mϑnð Þs s

ϑnðÞ¼ s ϑn0Znð Þs ; ϑn0 ¼ l

chA σ2ðÞþs

υð Þ¼ s, x υ1ð Þ s, 0 ;

υð Þ¼ s, x υ1ð Þ s, 0 ch½ �� θð Þs x

∂υð Þ s, x

Movement in two-link elements that occurs within elastic limits can be viewed as the movement of the driven point (link) from the movement of the leading point (link), which is affected by the previous links of the truss, for example, which perceive wind load. If, in the process of oscillation, the output link does not allow the input impulse to pass, then waves of disturbance are reflected from the end of the lines. Consider the case of a matched load when there are no reflected waves in the system and oscillations in the system do not affect the movement of the driven link due to the attached large mass. In this case, the boundary conditions are the fol-

υð Þ¼ s, l υ2ð Þs ; υð Þ¼ s, 0 υ1ð Þs ; σð Þ¼ s, l σ2ð Þs ; σð Þ¼ s, 0 σ1ð Þs ;

Here f2 is the sectional area of the line in front of the slave link of mass m; hn and Fс are coefficient of friction loss, proportional to the speed of movement, as well as the resistance force acting on the slave link; l is the length of the line. Together we solve (52)–(56) by performing the following transformations

;

1 s

Eυ1ð Þs θð Þs shA

;

ch½ � θð Þs l � Fcð Þs ϑnð Þs s: (58)

A ; A ¼ θð Þs l: (59)

(57)

chA σ2ðÞþs

½ � F sðÞþ hnυ2ðÞþs msυ2ð Þs :

After bringing similar members, we obtain the equation of motion of the

Ef 2

Substituting (58) into the last equation of system (57), we obtain an equation describing the stresses fluctuations in the force line in the vicinity of the slave link

; ZnðÞ¼ s

thA

2 ¼ υ1ð Þs

Eυ1ð Þs θð Þs shA

shA 1

FcðÞþs hnυ2ðÞþs msυ2ð Þs f 2

> 1 s

Eθð Þs

σ2ð Þs thA;

∂x ¼ � sσð Þ s, 0

sσ1ð Þ s, 0 sh½ � θð Þs x

E , (54)

θð Þs E : (55)

: (56)

$$\theta\_k(\mathfrak{s}) = \theta\_{k0} Z\_k(\mathfrak{s}); \theta\_{k0} = \frac{l}{Gr W\_{p2}}; Z\_k(\mathfrak{s}) = \frac{thA\_k}{A\_k}; A\_k = \theta\_k(\mathfrak{s}) l; \theta\_k(\mathfrak{s}) = \pm \sqrt{\frac{\rho}{G}}.\tag{62}$$

Comparing (15), (18), and (19), we can see that the processes of motion transfer in solid and liquid media can be described by similar equations. This is shown when analyzing the operation of the hydraulic drive [9, 35–37].

### 6. Lemma on the degree of distribution of force line parameters

Eqs. (47) and (48) make it possible to calculate the frequency characteristics of the system, i.e., determine the response of the model to the harmonic change in the speed of the lead link or the resistance force acting on the driven link.

For example, for υ1 � 0 and s=jω, we obtain the characteristic WF (jω), illustrating the influence of F on υ2, and the characteristic WFσ (jω), illustrating the influence of F on σ:

$$W\_F(jo) = \frac{\nu\_2(jo)}{F\_c(jo)} = -\frac{\mathfrak{d}\_n(jo)jo}{1 + h\_n \mathfrak{d}\_n(jo)jo + m\mathfrak{d}\_n(jo)(jo)};\tag{63}$$

$$W\_{F\sigma}(jao) = \frac{\sigma\_2(jao)}{F\_c(jao)} = \frac{1}{f\_2\left[1 + h\_n\theta\_n(jao)jao + m\theta\_n(jao)(jao)^2\right]}.\tag{64}$$

For F � 0, we obtain the frequency characteristics Wυ (jω), illustrating the effect of υ1 on υ2, and WFσ (jω), illustrating the influence of υ1 on σ2. So we have

$$W\_{\nu}(jo) = \frac{\nu\_2(jo)}{\nu\_1(jo)} = -\frac{ch^{-1}[\theta(jo)l]}{1 + h\_n\theta\_n(jo)jo + m\theta\_n(jo)(jo)^2},\tag{65}$$

$$W\_{F\sigma}(jao) = \frac{\sigma\_2(jao)}{\nu\_1(jao)} = \frac{h\_n + mjo}{f\_2 ch[\theta(jao)l] \left[1 + h\_n \theta\_n(jao)jo + m\theta\_n(jao)(jo)^2\right]}.\tag{66}$$

From (63) to (66), it can be seen that changes in the voltage and speed of movement of the output link are lagging behind changes in input impacts.

We introduce the notation α = l ω (ρ/E) 1/2.

Insofar as

$$Z\_n(ja) = \frac{th[\theta(ja)l]}{\theta(ja)l} = \frac{jtga}{ja} = \frac{tga}{a};\ ch(ja) = \cos a,\tag{67}$$

then

$$
\mathfrak{G}\_{\mathfrak{n}}(j a) = \mathfrak{G}\_{\mathfrak{n}}(a) = \mathfrak{G}\_{\mathfrak{n}0} Z\_{\mathfrak{n}}(a) \tag{68}
$$

and cosα are not complex functions.

The graph of the function Zп(α) is shown in Figure 4.

On the whole we conclude that at k = 1 α ! 0, Zп ! 1; at π/2 + kπ > α > π + kπ, Zп < 0. Here k = 0, 1, 2....n.

Eq. (58), given this, can be rewritten in the form

$$
\nu\_2(\mathfrak{s}) \left[ \mathbf{1} + h\_n \mathfrak{d}\_n(a) \mathfrak{s} + m \mathfrak{d}\_n(a) \mathfrak{s}^2 \right] = \nu\_1(\mathfrak{s}) \cos^{-1}(a) - F\_\varepsilon(\mathfrak{s}) \mathfrak{s} \mathfrak{d}\_n(a). \tag{69}
$$

If α ! 0, then Eq. (69) is reduced to the well-known equation describing dynamic processes in the mechanism with short lines of force:

$$
\sigma\_2(\mathfrak{s}) \left[ \mathbf{1} + h\_n \mathfrak{g}\_{n0} \mathfrak{s} + m \mathfrak{g}\_{n0} \mathfrak{s}^2 \right] = \nu\_1(\mathfrak{s}) - F\_c(\mathfrak{s}) \mathfrak{s} \mathfrak{g}\_{n0}.\tag{70}
$$

The breaks shown in Figure 4 are mathematically related to the function of tangent. For a real mechanism, this means that motion parameters are rebuilt. Apparently, in this instant, the form of oscillations changes abruptly. Below this feature is discussed in more detail.

The appearance of resonance is described by another expression that defines the conditions for the formation of the maximum amplitude of oscillations.

$$A\_F(\boldsymbol{\alpha}) = \frac{\mathfrak{d}\_n(\boldsymbol{a})\boldsymbol{\alpha}}{\sqrt{\left[\mathbbm{1} - m\mathfrak{d}\_n(\boldsymbol{a})\boldsymbol{\alpha}^2\right]^2 + \left[h\_n\mathfrak{d}\_n(\boldsymbol{a})\boldsymbol{\alpha}\right]^2}} = \left(\sqrt{\frac{\left[\mathbbm{1} - m\mathfrak{d}\_n(\boldsymbol{a})\boldsymbol{\alpha}^2\right]^2}{\left[\mathfrak{d}\_n(\boldsymbol{a})\boldsymbol{\alpha}^2\right]} + h\_n^2}\right)^{-1}.\tag{71}$$

Thus AF achieves its maximum when the condition

$$\frac{1 - m\theta\_n(a)\alpha^2}{\theta\_n(a)\alpha} = 0.\tag{72}$$

Let the mass of the load be m and the ratio of the mass of the rod with the cross-sectional area f to the mass of the load be a = lμ/m. Here μ is the linear mass

It is believed that the longitudinal tension of the rod during oscillations is balanced by the force of inertia of the load. This leads to the following condition at

¼ �m

At the top end, which is fixed we have y(0, t) = 0. At the initial time, the rod is stretched by the force F applied to the lower end and then without the initial speed

dy xð Þ , 0

t � � þ Bi sin pi

∂2 y ∂t2 � �

x¼l

φð Þ¼ x B cosð Þþ bx D sin ð Þ bx , (75)

t � � � � φð Þ x (76)

βtgβ ¼ a, (77)

: (73)

dt ¼ 0: (74)

x¼l

y xð Þ¼ :0 Fx

and parameter b values in the equation of the vibration modes

i�1

From the first boundary condition (41), it follows that B = 0. After that, from the second condition is the equation of frequencies

u xð Þ¼ , t X∞

in accordance with the initial conditions (74).

Ef ;

and, moreover, to the calculation of the constants Ai and Bi of the general

Ai cos pi

The solution of the problem is reduced to the calculation of the constant B, D,

Ef ∂y ∂x � �

Dynamic Stability of Open Two-Link Mechanical Structures

DOI: http://dx.doi.org/10.5772/intechopen.91045

of the rod.

Figure 5.

the lower end of the rod:

Cargo suspended on a rod.

is left to itself, so that

solution

17

We show that this condition is similar to the rule for determining natural frequencies. This rule was formulated by Babakov [22].

Consider the following problem. Let the rod hang vertically. At the end of the rod, a load is fixed. The load is assumed to be point (Figure 5).

#### Figure 4.

Change of function Zn of dimensionless parameter α: I is the range of admissible function values for systems with lumped parameters; II is the range of admissible values of the function for systems with distributed parameters.

Dynamic Stability of Open Two-Link Mechanical Structures DOI: http://dx.doi.org/10.5772/intechopen.91045

ϑnð Þ¼ jω ϑnð Þ¼ α ϑn0Znð Þ α (68)

2 � � ¼ υ1ðÞ�s Fcð Þs sϑn0: (70)

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 � mϑnð Þ α ω2 ½ �2

ϑnð Þ α ω ¼ 0: (72)

ϑnð Þ α ω2 ½ � þ h2

n

1 A

�1

: (71)

ð Þ� α Fcð Þs sϑnð Þ α : (69)

and cosα are not complex functions.

Truss and Frames - Recent Advances and New Perspectives

υ2ð Þs 1 þ hnϑnð Þ α s þ mϑnð Þ α s

feature is discussed in more detail.

Figure 4.

16

AFð Þ¼ ω ϑnð Þ α ω ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

1 � mϑnð Þ α ω2 ½ �2 þ ½ � hnϑnð Þ α ω 2 q ¼

Thus AF achieves its maximum when the condition

quencies. This rule was formulated by Babakov [22].

rod, a load is fixed. The load is assumed to be point (Figure 5).

Zп < 0. Here k = 0, 1, 2....n.

The graph of the function Zп(α) is shown in Figure 4.

2 � � ¼ υ1ð Þs cos �1

dynamic processes in the mechanism with short lines of force:

υ2ð Þs 1 þ hnϑn0s þ mϑn0s

Eq. (58), given this, can be rewritten in the form

On the whole we conclude that at k = 1 α ! 0, Zп ! 1; at π/2 + kπ > α > π + kπ,

If α ! 0, then Eq. (69) is reduced to the well-known equation describing

The breaks shown in Figure 4 are mathematically related to the function of tangent. For a real mechanism, this means that motion parameters are rebuilt. Apparently, in this instant, the form of oscillations changes abruptly. Below this

conditions for the formation of the maximum amplitude of oscillations.

1 � mϑnð Þ α ω2

We show that this condition is similar to the rule for determining natural fre-

Consider the following problem. Let the rod hang vertically. At the end of the

Change of function Zn of dimensionless parameter α: I is the range of admissible function values for systems with lumped parameters; II is the range of admissible values of the function for systems with distributed parameters.

The appearance of resonance is described by another expression that defines the

0s @

Let the mass of the load be m and the ratio of the mass of the rod with the cross-sectional area f to the mass of the load be a = lμ/m. Here μ is the linear mass of the rod.

It is believed that the longitudinal tension of the rod during oscillations is balanced by the force of inertia of the load. This leads to the following condition at the lower end of the rod:

$$E\xi \left(\frac{\partial \mathbf{y}}{\partial \mathbf{x}}\right)\_{\mathbf{x}=\mathbf{l}} = -m \left(\frac{\partial^2 \mathbf{y}}{\partial \mathbf{t}^2}\right)\_{\mathbf{x}=\mathbf{l}}.\tag{73}$$

At the top end, which is fixed we have y(0, t) = 0. At the initial time, the rod is stretched by the force F applied to the lower end and then without the initial speed is left to itself, so that

$$\text{hyp}(\mathbf{x}, \mathbf{0}) = \frac{F\mathbf{x}}{E\mathbf{f}} ; \frac{d\mathbf{y}(\mathbf{x}, \mathbf{0})}{dt} = \mathbf{0}. \tag{74}$$

The solution of the problem is reduced to the calculation of the constant B, D, and parameter b values in the equation of the vibration modes

$$\mathfrak{sp}(\mathfrak{x}) = B\cos\left(b\mathfrak{x}\right) + D\sin\left(b\mathfrak{x}\right),\tag{75}$$

and, moreover, to the calculation of the constants Ai and Bi of the general solution

$$u(\mathbf{x},t) = \sum\_{i=1}^{\infty} \left[ A\_i \cos \left( p\_i t \right) + B\_i \sin \left( p\_i t \right) \right] \boldsymbol{\uprho}(\mathbf{x}) \tag{76}$$

in accordance with the initial conditions (74). From the first boundary condition (41), it follows that B = 0. After that, from the second condition is the equation of frequencies

$$
\beta \text{tg}\beta = a,\tag{77}
$$

where β = al. Thus, the equation of the own modes of oscillations of the rod has the form

$$\mathfrak{q}\_k(\mathfrak{x}) = D\_k \sin \left( \frac{\beta\_k \mathfrak{x}}{l} \right)\_{, (k=1,2,3,\dots)} \tag{78}$$

7. Dynamic stability of rod systems

DOI: http://dx.doi.org/10.5772/intechopen.91045

Dynamic Stability of Open Two-Link Mechanical Structures

in [9, 29, 35–37].

functions

L�1

[29, 35].

19

[9, 29, 31, 35–37].

We have then

j j F1ð Þs ¼ 1

2πj

ðcþj∞

c�j∞

problem of ensuring sustainable functioning inevitably arises.

We algebraically decompose Eq. (58) into two. We have

υ1

ϑnð Þ α f 2σð Þs e

L�1

Then the originals (31) can be written in the form

Here α corresponds to the expression (84).

Wave phenomena take place in hydraulic, mechanical, electrical environments [4]. As shown above, wave processes take place in systems with lines of any length, but depending on the conditions, they can either be neglected or not ignored. If at the same time there is a transfer of energy to perform any effective work, then the

cos α ¼ υ2ðÞþs ϑnð Þ α f 2sσð Þs ; (85)

σð Þs f 2 ¼ FcðÞþs hnυ2ðÞþs msυ2ð Þs : (86)

F1ðÞ¼ s ϑnð Þ α f 2sσð Þs and F2ðÞ¼ s υ1ð Þs = cos α: (87)

1 2πj ðcþj∞

sσð Þs e

stds ¼ ϑnð Þ α f 2

dt ; (90)

dt : (91)

dσ dt :

(88)

c�j∞

j j F2ð Þs ¼ υ1ð Þt = cos α: (89)

dσ

dυ2

Publications devoted to the study of the stability of open-loop systems with distributed parameters in the presence of significant nonlinearities, where sufficiently precise criteria are stated, could not be found. Therefore, here outlines the main points of this issue, which were developed in more detail

The accuracy of the decomposition is easily verified by the inverse solution. Moving on to the originals of Eq. (58), we do the inverse transform Laplace of

stds ¼ ϑnð Þ α f 2

υ1ð Þt = cos α ¼ υ2ðÞþt ϑnð Þ α f 2

σð Þt f 2 ¼ FcðÞþt hnυ2ðÞþt m

The system of Eqs. (90, 91) may contain various nonlinearities (yield zone in the stress diagram, nonlinear friction, etc.) and is solved by the updated Runge-Kutta method [9, 38]. The admissibility of such a technique was checked by comparing the frequency characteristics constructed by formulas (63) to (66) and using the above method when introducing harmonic oscillations with different frequencies

In addition, given that the fluctuations of the speeds of movement and stresses (pressure) in mechanical and hydraulic systems can be described by similar equations, we checked the adequacy of the proposed method by means of full-scale and numerical experiments in an electric drive. The results had good convergence

In the process of modeling, it turned out that when Z < 0 (Figure 4), the solution becomes unstable. Figure 6 shows an example of the process of loss of

Here βk is the roots of Eq. (77).

The solution of Eq. (78) can be carried out graphically [21].

The lowest natural frequencies corresponding to these values are calculated by the formula

$$
\alpha = p\_1 = \frac{\beta\_1}{l} \sqrt{\frac{E\overline{f}}{\mu}}.\tag{79}
$$

Note that the linear mass of the rod μ = ρf. Expanding the coefficients, we obtain the original equation

$$
\beta \text{tg}\beta = \frac{\text{lf}\,\rho}{m}.\tag{80}
$$

We now turn to Eq. (79) and divide the numerator of the right side by the denominator

$$\text{Ef } \frac{\sqrt{\rho/E}}{\text{tg}a} = ma. \tag{81}$$

We will still carry out a number of transformations. We have

$$\text{Efl}\frac{\sqrt{\rho/E}}{m} = \text{log}\mathbf{a}; \frac{f\mathbf{l}}{m} = \frac{\text{log}\mathbf{a}}{\sqrt{E\rho}}.\tag{82}$$

After multiplying both sides of the last equation by ρ and after performing the corresponding transformations, we get

$$\frac{\rho \text{fl}}{m} = a \text{tg}a.\tag{83}$$

Since here the parameters α and β are equivalent, it can be argued that the roots of Eqs. (72) and (80) are the same. This is confirmed by the results of calculations.

The results obtained make it possible to formulate a lemma on the degree of distribution of the parameters of power lines. But for this, we introduce the notation

$$a = \operatorname{lco} \sqrt{\mathfrak{p}/\chi},\tag{84}$$

where χ is the elastic modulus of the material of the force line.

We state the lemma as follows. If the parameters of the mechanical two-link system, characterized by the oscillation frequency ω, length l, density ρ, and the elastic modulus of the material of the force line χ connecting these links, are such that magnitude of the dimensionless coefficient α lies in the interval 0 ≤ α ≤ 1, then the wave processes in the lines of force can be neglected.

This lemma is also valid for systems where torsional vibrations of rods and vibrations in hydraulic systems take place. The criterion on the degree of distribution of the system parameters was first described in the book [29].

## 7. Dynamic stability of rod systems

where β = al.

the formula

the original equation

denominator

notation

18

lines of force can be neglected.

Here βk is the roots of Eq. (77).

Truss and Frames - Recent Advances and New Perspectives

Thus, the equation of the own modes of oscillations of the rod has the form

l � �

The lowest natural frequencies corresponding to these values are calculated by

l

Note that the linear mass of the rod μ = ρf. Expanding the coefficients, we obtain

βtgβ ¼ lf ρ

We now turn to Eq. (79) and divide the numerator of the right side by the

ffiffiffiffiffiffiffiffi ρ=E p

m ¼ lωtgα; fl

ρfl

After multiplying both sides of the last equation by ρ and after performing the

Since here the parameters α and β are equivalent, it can be argued that the roots of Eqs. (72) and (80) are the same. This is confirmed by the results of calculations. The results obtained make it possible to formulate a lemma on the degree of distribution of the parameters of power lines. But for this, we introduce the

α ¼ lω ffiffiffiffiffiffiffi

This lemma is also valid for systems where torsional vibrations of rods and vibrations in hydraulic systems take place. The criterion on the degree of distribu-

We state the lemma as follows. If the parameters of the mechanical two-link system, characterized by the oscillation frequency ω, length l, density ρ, and the elastic modulus of the material of the force line χ connecting these links, are such that magnitude of the dimensionless coefficient α lies in the interval 0 ≤ α ≤ 1, then the wave processes in the

where χ is the elastic modulus of the material of the force line.

tion of the system parameters was first described in the book [29].

m ¼ lωtgα ffiffiffiffiffi

Ef

We will still carry out a number of transformations. We have

ffiffiffiffiffiffiffiffi ρ=E p

Efl

corresponding transformations, we get

ffiffiffiffiffi Ef μ

s

ω ¼ p1 ¼ β1

, ð Þ k¼1,2,3, … :

: (79)

m : (80)

tgα ¼ mω: (81)

m ¼ αtgα: (83)

ρ=χ p , (84)

Eρ p : (82)

(78)

φkð Þ¼ x Dk sin βkx

The solution of Eq. (78) can be carried out graphically [21].

Wave phenomena take place in hydraulic, mechanical, electrical environments [4]. As shown above, wave processes take place in systems with lines of any length, but depending on the conditions, they can either be neglected or not ignored. If at the same time there is a transfer of energy to perform any effective work, then the problem of ensuring sustainable functioning inevitably arises.

Publications devoted to the study of the stability of open-loop systems with distributed parameters in the presence of significant nonlinearities, where sufficiently precise criteria are stated, could not be found. Therefore, here outlines the main points of this issue, which were developed in more detail in [9, 29, 35–37].

We algebraically decompose Eq. (58) into two. We have

$$\frac{\nu\_1}{\cos a} = \nu\_2(s) + \theta\_n(a) f\_2 s \sigma(s);\tag{85}$$

$$
\sigma(\mathfrak{s})f\_2 = F\_\mathfrak{c}(\mathfrak{s}) + h\_n \nu\_2(\mathfrak{s}) + m \mathfrak{s} \nu\_2(\mathfrak{s}).\tag{86}
$$

Here α corresponds to the expression (84).

The accuracy of the decomposition is easily verified by the inverse solution. Moving on to the originals of Eq. (58), we do the inverse transform Laplace of functions

$$F\_1(\mathfrak{s}) = \theta\_n(a) f\_{\mathfrak{z}} \mathfrak{s} \sigma(\mathfrak{s}) \text{ and } F\_2(\mathfrak{s}) = \nu\_1(\mathfrak{s}) / \cos a. \tag{87}$$

We have then

$$L^{-1}|F\_1(s)| = \frac{1}{2\pi j} \int\_{c - j\circ\sigma}^{c + j\circ\sigma} \theta\_n(a) f\_2 \sigma(s) e^{\mathfrak{s}t} ds = \theta\_n(a) f\_2 \frac{1}{2\pi j} \int\_{c - j\circ\sigma}^{c + j\circ\sigma} s\sigma(s) e^{\mathfrak{s}t} ds = \theta\_n(a) f\_2 \frac{d\sigma}{dt}.\tag{88}$$

$$L^{-1}|F\_2(\mathfrak{s})| = \nu\_1(\mathfrak{t})/\cos a. \tag{89}$$

Then the originals (31) can be written in the form

$$\nu\_1(t) / \cos a = \nu\_2(t) + \theta\_n(a) f\_2 \frac{d\sigma}{dt};\tag{90}$$

$$
\sigma(t)f\_2 = F\_c(t) + h\_n v\_2(t) + m\frac{d\nu\_2}{dt}.\tag{91}
$$

The system of Eqs. (90, 91) may contain various nonlinearities (yield zone in the stress diagram, nonlinear friction, etc.) and is solved by the updated Runge-Kutta method [9, 38]. The admissibility of such a technique was checked by comparing the frequency characteristics constructed by formulas (63) to (66) and using the above method when introducing harmonic oscillations with different frequencies [29, 35].

In addition, given that the fluctuations of the speeds of movement and stresses (pressure) in mechanical and hydraulic systems can be described by similar equations, we checked the adequacy of the proposed method by means of full-scale and numerical experiments in an electric drive. The results had good convergence [9, 29, 31, 35–37].

In the process of modeling, it turned out that when Z < 0 (Figure 4), the solution becomes unstable. Figure 6 shows an example of the process of loss of

#### Figure 6.

Loss of stable operation in the mechanical element during longitudinal movement.

#### Figure 7.

Zones of steady (shaded) and unstable operation of the mechanical system of longitudinal movement.

dynamic stability in a mechanical element with longitudinal vibrations. For a truss, this means breaking one of the rods.

The areas of dynamic stability for mechanical elements with longitudinal vibrations are shown in Figure 7.

Author details

21

Leonid Kondratenko\* and Lubov Mironova

provided the original work is properly cited.

Moscow Aviation Institute (SNRU), Moscow, Russia

Dynamic Stability of Open Two-Link Mechanical Structures

DOI: http://dx.doi.org/10.5772/intechopen.91045

\*Address all correspondence to<EMAIL_ADDRESS>
© 2020 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium,

### 8. Conclusions

In trusses under the influence of variable loads, vibrations occur periodically in different elements, characterized by fluctuations in speed and stress. Under certain conditions, due to wave motions in the rods, the shape of the oscillations may change, i.e., lost stability of motion. At this instant, the destruction of the carrier element will occur. The proposed chapter considers the conditions for the occurrence of such an event.

Dynamic Stability of Open Two-Link Mechanical Structures DOI: http://dx.doi.org/10.5772/intechopen.91045


**1. Introduction**

With the vast popularity of social networks, people tend to express their emotions and share their experiences online through posting images [1], which promotes the study of the principles of human emotion and the analysis and estimation of human behavior. Recently, with the wide application of convolution neural networks (CNNs) in emotion prediction, numerous studies [2–4] have proved the excellent ability of CNN to recognize the emotional features of images.

Based on the theory that the emotional cognition of a stimulus attracts more human attention [5], some researchers enriched emotional prediction with saliency detection or instance segmentation to extract more concrete emotional features [6–8]. Yang et al. [9] put forward the "Affective Regions" which are objects that convey significant sentiments, and proposed three fusion strategies for image features from the original image and "Affective Regions". Alternatively, Wu et al. [8] utilized saliency detection to enhance the local features, improving the classification performance to a large margin.

"Affective Regions" or Local features in images play a crucial role in image emotion, and the above methods can effectively improve classification accuracy. However, although these methods have achieved great success, there are still some drawbacks. They focused on improving visual representations and ignored emotional effectiveness of objects, which leads to a non-tendential feature enhancement. For example, in an image expressing a

**Citation:** Wu, L.; Zhang, H.; Deng, S.; Shi, G.; Liu, X. Discovering Sentimental Interaction via Graph Convolutional Network for Visual Sentiment Prediction. *Appl. Sci.* **2021**, *11*, 1404. https://doi.org/10.3390/ app11041404

Academic Editor: Byung-Gyu Kim

Received: 30 December 2020 Accepted: 29 January 2021 Published: 4 February 2021

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

positive sentiment, positivity is generated by interaction among objects. Separating objects and directly merging the features will lose much of the critical information of image.

Besides, they also introduce a certain degree of noise, which leads to the limited performance improvement obtained through visual feature enhancement. For example, in human common sense, "cat" tends to be a positive categorical word. As shown in Figure 1a,b, when "cat" forms the image with other neutral or positive objects, the image tends to be more positive, consistent with the conclusion that local features can improve accuracy. In the real world, however, there are complex images, as shown in Figure 1c,d, "cat" can be combined with other objects to express opposite emotional polarity, reflecting the effect of objects on emotional interactions. Specifically, in Figure 1d, the negative sentiment is not directly generated by the "cat" and "injector", but the result of the interaction between the two in the emotional space. Indiscriminate feature fusion of such images will affect the performance of the classifier.

**Figure 1.** Examples from EmotionROI dataset and social media: We use a graph model to describe the sentimental interaction between objects and the double arrow means the interaction in the process of human emotion reflection.

To address the abovementioned problems, we design a framework with two branches, one of which uses a deep network to extract visual emotional features in images. The other branch uses GCN to extract emotional interaction features of objects. Specially, we utilize Detectron2 to obtain the object category, location, and additional information in images. And then, SentiWordNet [10] is selected as an emotional dictionary to mark each category word with emotional intensity value. Based on the above information, we use the sentimental value of objects and visual characteristics in each image to build the corresponding graph model. Finally, we employ GCN to update and transmit node features, generate features after object interaction, which, together with visual components, serve as the basis for sentiment classification.

The contributions of this paper can be summarized as follows:

1. We propose an end-to-end image sentiment analysis framework that employs GCN to extract sentimental interaction characteristics among objects. The proposed model makes extensive use of the interaction between objects in the emotional space rather than directly integrating the visual features.

2. We design a method to construct graphs over images by utilizing Detectron2 and SentiWordNet. Based on the public datasets analysis, we leverage brightness and texture as the features of nodes and the distances in emotional space as edges, which can effectively describe the appearance characteristics of objects.

3. We evaluate our method on five affective datasets, and our method outperforms previous high-performing approaches.

We make all programs of our model publicly available for research purposes https: //github.com/Vander111/Sentimental-Interaction-Network.

#### **2. Related Work**

#### *2.1. Visual Sentiment Prediction*

Existing methods can be classified into two groups: dimensional spaces and categorical states. Dimensional spaces methods employ valence-arousal space [11] or activity-weightheat space [12] to represent emotions. On the contrary, categorical states methods classify emotions into corresponding categories [13,14], which is easier for people to understand, and our work falls into categorical states group.

Feature extraction is of vital importance to emotion analysis, various kinds of features may contribute to the emotion of images [15]. Some researchers have been devoting themselves to exploring emotional features and bridging the "affective gap", which can be defined as the lack of coincidence between image features and user emotional response to the image [16]. Inspired by art and psychology, Machajdik and Hanbury [14] designed low-level features such as color, texture, and composition. Zhao et al. [17] proposed extensive use of visual image information, social context related to the corresponding users, the temporal evolution of emotion, and the location information of images to predict personalized emotions of a specified social media user.

With the availability of large-scale image datasets such as ImageNet and the wide application of deep learning, the ability of convolutional neural networks to learn discriminative features has been recognized. You et al. [3] fine-tuned the pre-trained AlexNet on ImageNet to classify emotions into eight categories. Yang et al. [18] integrated deep metric learning with sentiment classification and proposed a multi-task framework for affective image classification and retrieval.

Sun et al. [19] discovered affective regions based on an object proposal algorithm and extracted corresponding in-depth features for classification. Later, You et al. [20] adopted an attention algorithm to utilize localized visual features and got better emotional classification performance than using global visual features. To mine emotional features in images more accurately, Zheng et al. [6] combined the saliency detection method with image sentiment analysis. They concluded that images containing prominent artificial objects or faces, or indoor and low depth of field images, often express emotions through their saliency regions. To enhance the work theme, photographers blurred the background to emphasize the main body of the picture [14], which led to the birth of close-up or low-depth photographs. Therefore, the focus area in low-depth images fully expresses the information that the photographer and forwarder want to tell, especially emotional information.

On the other hand, when natural objects are more prominent than artificial objects or do not contain faces, or open-field images, emotional information is usually not transmitted only through their saliency areas. Based on these studies, Fan et al. [7] established an image dataset labeled with statistical data of eye-trackers on human attention to exploring the relationship between human attention mechanisms and emotional characteristics. Yang et al. [9] synthetically considered image objects and emotional factors and obtained better sentiment analysis results by combining the two pieces of information.

Such methods make efforts in extracting emotional features accurately to improve classification accuracy. However, as an integral part of an image, objects may carry emotional information. Ignoring the interaction between objects is unreliable and insufficient. This paper selects the graph model and graph convolution network to generate sentimental interaction information and realize the sentiment analysis task.

#### *2.2. Graph Convolutional Network(GCN)*

The notion of graph neural networks was first outlined in Gori et al. [21] and further expound in Scarselli et al. [22]. However, these initial methods required costly neural "message-passing" algorithms to convergence, which was prohibitively expensive on massive data. More recently, there have been many methods based on the notion of GCN, which originated from the graph convolutions based on the spectral graph theory of Bruna et al. [23]. Based on this work, a significant number of jobs were published and attracted the attention of researchers.

Compared with the deep learning model introduced above, the graph model virtually constructs relational models. Chen et al. [24] combined GCN with multi-label image recognition to learn inter-dependent object information from labels. A novel re-weighted strategy was designed to construct the correlation matrix for GCN, and they got a higher accuracy compared with many previous works. However, this method is based on the labeled objects information from the dataset, which needs many human resources.

In this paper, we employ the graph structure to capture and explore the object sentimental correlation dependency. Specifically, based on the graph, we utilize GCN to propagate sentimental information between objects and generate corresponding interaction features, which is further applied to the global image representation for the final image sentiment prediction. Simultaneously, we also designed a method to build graph models from images based on existing image emotion datasets and describe the relationship features of objects in the emotional space, which can save a lot of workforce annotation.


**19. Conclusions**

Australia has a robust and reliable set of health statistics. This is the result of many decades of national governance cooperation, resourcing, and effort. The ongoing commitment of resources and collaboration among stakeholders continues to be essential to ensure a robust evidence base to inform policy and practice, based on nationally consistent data standards, and to underpin research efforts, into the future. Some specific potential improvements have been highlighted, and the full potential of data linkage has yet to be achieved.

People provide information about themselves and their health in many settings and are often unaware that this information provides input to health statistics which, in turn, improves health and health services [47]. Respecting individuals' data remains at the heart of the health statistics effort, and using it as well as possible is a key responsibility for the statistical community.

**Author Contributions:** Conceptualization, R.M., N.F. and J.G.; investigation, R.M., N.F., J.G.; writing— review and editing, R.M., N.F., J.G. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Not applicable.

**Conflicts of Interest:** The authors declare no conflict of interest.


**1. Antibiotic resistance as a global threat**

The global burden of antibiotic resistance is mounting continuously; preferably it piles up the pressure on veterinary medicine and on human. The WHO made a landmark by promoting and declaring AMR as a global health concern. The agenda of global health concerns are at the developmental stages, for example, a book named as *The Evolving Threat of Antimicrobial Resistance: Options for Action* is a precious addition to the archive [1]. Currently, the world is experiencing dramatic pre-antibiotic era, and many of the untreated infection emerge on a large-scale; clinicians often encounter many patients with such infections that normally reported as PDR or MDR bacteria by many laboratories and not responding to already available therapeutics. It has been estimated that yearly about two million people acquire vulnerable infections just because of these antibiotic-resistant pathogens, and as a result of this, about 23,000 people die according to Centers for Disease Control and Prevention (CDC) [2].

In a historical perspective, antibiotic resistance is a mounting and compelling concern. New types of antibiotic-resistant bacteria are taking control of ancient drugs. We may be entering the post-antibiotic era, because of increased persistence, spread, and the emergence of superbugs. It has been reported that annually, in the USA, about 99,000 deaths are caused by antibiotic-resistant pathogen-related hospital-acquired infections [3]. While in America, the annual death rate is about 50,000 caused by two usual HAIs, known as sepsis and pneumonia, which cost around \$8 billion to the economy of the USA. The patients infected with bacterial strains that are resistant to antibiotics must stay in the hospital minimum for 13 days, which adds to 8 million days annually. An annual report of the cost of economy loss with regard to a productivity loss of around \$35 billion has been demonstrated within healthcare settings [3].

### **2. Causes of antibiotic resistance**

Currently, the multifarious causes of resistance constitute many factors including improper use and regulations, lack of awareness, aberrant antibiotic usage, the use of antibiotics as a growth promoter in livestock as well as in poultry for infection control, and online marketing [4]. Fundamentally, the reason behind the resistance evolution is the improper and excessive use of antimicrobials. The powerful drivers of antibiotic resistance include infection control standards, sanitation system, drug quality, water hygiene systems, diagnostics and therapeutics, and migration or travel quarantine. Genetic mutations and exchange of genetic material between organisms play a key role in the distribution of antibiotic resistance [5]. MDR organisms in hospital wastes are associated with public health illnesses because they are ultimately disseminated to humans. In this regard, recently a study has been conducted in Pakistan to find the occurrence of ESBL producing *K. pneumoniae* in hospital wastes including hospital sludge and wastewater, operation theater waste. They found the significant percentage of extended-spectrum β-lactamases (ESBL) producing MDR *K. pneumoniae* in these wastes [6]. Similarly another study conducted by [7] reported the patterns of antibiotic-resistant *K. pneumoniae* in clinical isolates with special reference to fluoroquinolones, depicting an alarming threat of antibiotic resistance among *K. pneumoniae*-related nosocomial infections.

#### **3. Carbapenems**

Carbapenems are effective β-lactam antimicrobials and have very potent efficacy against many ESBL-producing bacteria and are also administered intravenously.

**63**

**Table 1.**

*Carbapenem Resistance: Mechanisms and Drivers of Global Menace*

In order to treat bacterial infections, carbapenems are considered as the most reliable and the last resort class of antimicrobials. Carbapenem agent has a very unique structure, usually defined by carbapenem coupled to B-lactam ring, which provide protection against the majority of b-lactamases as well as metallo-b-lactamases, and thus possess extended antibacterial activity [8]. Carbapenems work by penetrating the cell wall of bacteria, binding with penicillin-binding proteins (PBPs), and result in inactivation of intracellular autolytic inhibitor enzymes, ultimately killing the

In addition, carbapenems mainly target "transpeptidase inhibition enzyme" during bacterial cell wall synthesis, preventing peptide cross-linking activity, leading to enhanced autolytic activity, and thus resulting in cell death. Therefore, carbapenems are considered as effective antimicrobials to treat life-threatening and invasive infections due to their "concentration-independent killing effect" on

Carbapenemases are versatile b-lactamases, having the capability to hydrolyze carbapenems, cephalosporins, penicillins, and monobactams. Carbapenemases typically belong to two molecular families, namely, "metallo-carbapenemases" in which activity is inhibited by EDTA, used zinc molecule at their active sites, and "serine-based carbapenemases" in which activity is not inhibited by EDTA rather used serine residues at their active sites and inactivated through β-lactamase inhibi-

β-Lactamases are classified based on two properties: functional and molecular ones. Functional classification was proposed by a scientist "Bush" in 1988, who classified β-lactamases into four functional groups namely, groups 1–4. Carbapenems fall under subgroup the 2f and group 3 [12]. Later on another scientist, Rasmussen, suggested that group 3 can be further divided into three functional subgroups on

The molecular classification was proposed by scientist "Frere" and colleagues, who classified carbapenemases into class A, class B, and class D car-

Class A carbapenemases require a serine active site at position number 70 in Ambler numbering system, fall under the group 2f, and have the ability to hydro-

Class A SME, NMC, KPC, IMI, GES All *Enterobacteriaceae*, rarely *P. aeruginosa* Class B VIM, SPM, GIM, IMP *Acinetobacter* species*, P. aeruginosa*,

*Enterobacteriaceae*

lyze carbapenems, penicillins, aztreonam, and cephalosporins [14].

**Classification Enzymes Common bacteria**

Class D OXA *Acinetobacter* species

*DOI: http://dx.doi.org/10.5772/intechopen.90100*

bacterial cell.

infecting bacteria [9, 10].

**4. Carbapenemases**

tors like tazobactam and clavulanic acid [11].

the basis of substrate specificity [13].

Subclass B1 VIM-2, IMP-1, SPM-1, CcrA and BcII

Subclass B3 Gob-1, FEZ-1, CAU-1 & L1

*Molecular classification scheme of carbapenemases [16].*

Subclass B2 Sfh-1, CphA

bapenemases (**Table 1**).

#### *Carbapenem Resistance: Mechanisms and Drivers of Global Menace DOI: http://dx.doi.org/10.5772/intechopen.90100*

In order to treat bacterial infections, carbapenems are considered as the most reliable and the last resort class of antimicrobials. Carbapenem agent has a very unique structure, usually defined by carbapenem coupled to B-lactam ring, which provide protection against the majority of b-lactamases as well as metallo-b-lactamases, and thus possess extended antibacterial activity [8]. Carbapenems work by penetrating the cell wall of bacteria, binding with penicillin-binding proteins (PBPs), and result in inactivation of intracellular autolytic inhibitor enzymes, ultimately killing the bacterial cell.

In addition, carbapenems mainly target "transpeptidase inhibition enzyme" during bacterial cell wall synthesis, preventing peptide cross-linking activity, leading to enhanced autolytic activity, and thus resulting in cell death. Therefore, carbapenems are considered as effective antimicrobials to treat life-threatening and invasive infections due to their "concentration-independent killing effect" on infecting bacteria [9, 10].