**6. References**

288 Mechanical Engineering

It is proposed in this paper the design of a winding mechanism for amorphous strips used in magnetic transformer´s cores, its general dimensions are specified in the drawing in Figure 12, and it´s assemble with the personally designed equipment is completely possible. The components and parts designs are based on our own experience in building these equipments and on our investigations on the production of micro and nano-materials (Ozols et al., 1999; Pagnola, 2009; Muraca et al., 2009), as well as other author's technical considerations in the fabrication of different products for industrial magnetic packages as

shown in Figure N. 13. (Croat, 1992; Kurokawa, et al. 1999) were considered.

Fig. 13. Fe78 Si13B9 amorphous strips used in magnetic cores, and industrial magnetic

Fig. 12. General drawing of mechanical parts.

package.

**5. Conclusion**

**13**

*Argentina*

**Free Vibration Analysis of Centrifugally**

*Universidad Nacional del Sur, UNS, Departamento de Ingeniería,*

*Consejo Nacional de Investigaciones Científicas y Técnicas, CONICET,*

 *Instituto de Mecánica Aplicada, IMA,*

**Stiffened Non Uniform Timoshenko Beams**

Diana V. Bambill, Daniel H. Felix, Raúl E. Rossi and Alejandro R. Ratazzi

Rotating beams – like structures are widely used in many engineering fields and are of great interest as they can be used to model blades of wind turbines, helicopter rotors, robotic manipulators, turbo-machinery and aircraft propellers. The governing differential equations of motion in free vibration of a non-uniform rotating Timoshenko beam, with general elastic restraints at the ends are solved using the differential quadrature method, (Bellman & Roth, 1986; Felix et al., 2008, 2009). The equations of motion are derived to include the effects of shear deformation, rotary inertia, hub radius, ends elastically restrained and non-uniform variation of the cross-sectional area of the beam. The presence of a centrifugal force due to the rotational motion is considered as Banerjee has developed, using Hamilton's principle to capture the centrifugal stiffening arising in fast rotating structures, (Banerjee, 2001). With the proposed model, a great number of different situations are admitted to be solved. Particular cases with classical restraints can be deduced for limiting values of the rigidities. Also step

The natural vibration frequencies and mode shapes of rotating beams have been a topic of interest and have received considerable attention. A large number of researchers have studied the dynamic behavior of rotating uniform or tapered Euler-Bernoulli beams. (Yang el al., 2004; Özdemir & Kaya, 2006; Lin & Hsiao, 2001). Banerjee derived the dynamic stiffness matrix of a rotating Bernoulli-Euler beam using the Frobenius method of solution in power series and he includes the presence of an axial force at the outboard end of the

Not so many studies have tackled the problem of rotating beams taking into account rotary inertia, shear deformation and their combined effects, hub radius and ends elastically restrained, (Bambill et al., 2010). In applications where the rotary inertia and the shear deformation effects are not significant, an analysis based on the Euler–Bernoulli beam theory can be used. However, Timoshenko theory allows describing the vibration of short beams, sandwich composite beams or high modes of a slender beam, (Rossi et al., 1991; Seon et al., 1999). (Banerjee et al., 2006) investigated the free bending vibration of rotating tapered Timoshenko beams by the dynamic stiffness method. (Ozgumus & Kaya, 2010) used the Differential Transform Method for free vibration analysis of a rotating, tapered Timoshenko

changes in cross-section are considered (Naguleswaran, 2004).

beam in addition to the existence of the usual centrifugal (Banerjee, 2000).

**1. Introduction**

beam.