tunable fluid end embodiments comprise a family , each family member comprising a fluid end housing with at least one installed tunable component chosen from : tunable check valve assemblies , tunable valve seats , tunable radial arrays and / or tunable plunger seals . installing one or more tunable check valve assemblies , for example , facilitates selective attenuation of valve - generated vibration at its source . the likelihood of fluid end failures associated with fatigue cracking and / or corrosion fatigue is thereby reduced . adding tunable valve seats , tunable radial arrays and / or plunger seals to tunable check valve assemblies in a fluid end further facilitates optimal damping and / or selective attenuation of vibration at one or more predetermined ( and frequently - localized ) fluid end resonant frequencies . optimized vibration attenuation ( via , e . g ., optimized fluid end damping ) is provided by altering resonant frequencies in each tunable component in relation to one or more ( measured or estimated ) fluid end resonant frequencies and / or tunable component resonant frequencies . in general , a tunable ( suction or discharge ) check valve of the invention may comprise , for example , a combination of a tunable check valve assembly / tunable radial array 99 ( see , e . g ., fig1 ) and a tunable valve seat 20 or a tunable valve seat 389 ( see , e . g ., fig7 and 11 ). details of the structure and functions of each component are provided herein both separately and as combined with other components to obtain synergistic benefits contributing to longer pump service life . fig1 and 2 schematically illustrate an invention embodiment of a tunable check valve assembly / tunable radial array 99 substantially symmetrical about a longitudinal axis . illustrated components include a valve body 10 , an adjustable preload flange 30 , and a plurality of viscoelastic body elements 50 . check valve body 10 , in turn , comprises a peripheral groove 12 ( see fig2 ) spaced apart by an annular ( central ) reservoir 16 from a longitudinal guide stem 14 , groove 12 being responsive to longitudinal compressive force . a plurality of viscoelastic body elements 50 comprises an annular ( central ) reservoir element 52 coupled to a ( peripheral ) groove element 54 by a plurality of ( optional ) radial fenestration elements 56 ( in fenestrations 18 ) to form a tunable radial array . groove element 54 functions as a vibration damper and valve seal , comprising at least one circumferential tubular area 58 . responsiveness of groove 12 to longitudinal compressive force is characterized in part by damping of groove wall 11 / 13 / 15 vibrations . such damping is due in part to out - of - phase vibrations in proximal groove wall 13 and distal groove wall 11 which are induced by longitudinal compressive force . such out - of - phase vibrations will cause various groove - related dimensions to vary with longitudinal compressive force , thereby indicating the responsiveness of groove 12 to such force ( see , for example , the dimension labeled a in fig2 ). each phase shift , in turn , is associated with differences in the coupling of proximal groove wall 13 to guide stem 14 ( indirectly via longitudinal groove wall 15 and radial reservoir floor 19 ) and the coupling of distal groove wall 11 to guide stem 14 ( directly via radial reservoir floor 19 ). note that longitudinal groove wall 15 may comprise fenestrations 18 , thereby increasing the responsiveness of groove 12 to longitudinal compressive force on tunable check valve assembly 99 . referring to fig1 - 3 , adjustable preload flange 30 extends radially from guide stem 14 ( toward peripheral reservoir wall 17 ) over , for example , about 20 % to about 80 % of viscoelastic reservoir element 52 ( see fig3 ). adjustable preload flange 30 thus imposes an adjustable annular shear preload over an annular constrained area 62 of viscoelastic reservoir element 52 to achieve at least a first predetermined assembly resonant frequency substantially replicating a ( similar ) measured or estimated resonant frequency ( e . g ., a pump housing resonant frequency ). note that an adjacent annular unconstrained area 60 of viscoelastic reservoir element 52 remains open to pumped fluid pressure . note also that adjustable preload flange 30 may be adjusted in effective radial extent and / or longitudinal position . note further that annular constrained area 62 and annular unconstrained area 60 are substantially concentric and adjacent . thus , for a tunable suction valve subject to longitudinal ( i . e ., distally - directed ) compressive constraint applied via preload flange 30 to annular constrained area 62 , annular unconstrained area 60 will tend to move ( i . e ., extrude ) proximally relative to area 62 . the oppositely - directed ( i . e ., countercurrent ) movements of constrained and unconstrained annular areas of viscoelastic reservoir element 52 create a substantially annular area of shear stress . finally , each circumferential tubular area 58 is substantially filled with at least one shear - thickening material 80 ( see fig5 ) chosen to achieve at least a second predetermined assembly resonant frequency similar , for example , to the first predetermined assembly resonant frequency ). note that fig5 schematically represents a partially - sectioned view of an instantaneous configuration of the shear - thickening material 80 within circumferential tubular area 58 . referring to fig1 and 2 in greater detail , a tunable check valve assembly / tunable radial array embodiment 99 comprises viscoelastic body elements 50 which comprise , in turn , reservoir ( central ) element 52 coupled to groove ( peripheral ) element 54 via radial fenestration ( tension ) elements 56 . elements 52 , 54 and 56 are disposed in ( i . e ., integrated with and / or lie substantially in ) reservoir 16 , groove 12 and fenestrations 18 respectively to provide a tuned radial array having at least a third predetermined resonant frequency . an adjustable preload flange 30 is coupled to guide stem 14 and contacts viscoelastic reservoir element 52 in reservoir 16 to impose an adjustable annular constraint on viscoelastic reservoir element 52 for achieving at least a first predetermined assembly resonant frequency substantially similar to , for example , a measured resonant frequency ( e . g ., a pump housing resonant frequency ). such adjustable annular constraint imposes an adjustable shear preload between constrained annular area 62 and unconstrained annular area 60 . tunable check valve assembly 99 may additionally comprise at least one circumferential tubular area 58 in groove element 54 residing in groove 12 , each tubular area 58 being substantially filled with at least one shear - thickening material 80 chosen to achieve at least a second predetermined assembly resonant frequency similar , for example , to the first predetermined assembly resonant frequency ). the above embodiment may be installed in a pump housing having a measured housing resonant frequency ; the measured housing resonant frequency may then be substantially replicated in the ( similar ) first predetermined resonant frequency of the tunable check valve assembly . such a combination would be an application of an alternate embodiment . an analogous tuning procedure may be followed if the tunable check valve assembly of the second embodiment is installed in a pump having a ( similar or different ) resonant frequency substantially equal to the second predetermined resonant frequency . this synergistic combination would broaden the scope of the valve assembly &# 39 ; s beneficial effects , being yet another application of the invention &# 39 ; s alternate embodiment . note that preload flange 30 may have a non - cylindrical periphery 32 for imposing on viscoelastic reservoir element 52 an adjustable annular shear preload having both longitudinal and transverse components . note further that the periphery of adjustable preload flange 30 , if cylindrical , predisposes a tunable check valve assembly to substantially longitudinal shear damping with each longitudinal distortion of check valve body 10 associated with valve closure . the character of such shear damping depends , in part , on the longitudinal position of the preload flange . examples of different longitudinal positions are seen in fig4 , which schematically illustrates the flange 30 ′ longitudinally displaced from flange 30 ″. further , as shown in fig4 , the convex periphery of a longitudinally adjusted preload flange 30 ′ or 30 ″ may introduce shear damping of variable magnitude and having both longitudinal and transverse components . such damping may be beneficial in cases where significant transverse valve - generated vibration occurs . to clarify the placement of viscoelastic body elements 50 , labels indicating the portions are placed on a sectional view in fig2 and 3 . actual placement of viscoelastic body elements 50 in valve body 10 ( see fig1 ) may be by , for example , casting viscoelastic body elements 50 in place , or placing viscoelastic body elements 50 ( which have been precast ) in place during layer - built or welded fabrication . the tunable check valve assembly embodiment of the invention is intended to represent check valve body 10 and viscoelastic body elements 50 as complementary components at any stage of manufacture leading to functional integration of the two components . to enhance scavenging of heat due to friction loss and / or hysteresis loss , shear - thickening material 80 and / or viscoelastic body elements 50 may comprise one or more polymers which have been augmented with nanoparticles and / or graphene 82 ( see , e . g ., fig5 ). nanoparticles and / or graphene may be invisible to the eye as they are typically dispersed in a colloidal suspension . hence , they are schematically represented by cross - hatching 82 in fig5 . nanoparticles may comprise , for example , carbon forms ( e . g ., graphene ) and / or metallic materials such as copper , beryllium , titanium , nickel , iron , alloys or blends thereof . the term nanoparticle may conveniently be defined as including particles having an average size of up to about 2000 nm . see , e . g ., the &# 39 ; 320 patent . fig6 is a schematic illustration of an exploded partially - sectioned 2 - dimensional view of major components of a pump fluid end subassembly 88 , together with graphical aids and brief explanatory comments on component functions . the schematically - illustrated subassembly 88 comprises a pumping chamber 74 within a subassembly ( pump ) housing 78 , the pumping chamber 74 being in fluid communication with a suction bore 76 , a discharge bore 72 , and a piston / plunger bore 70 . note that piston / plunger bore 70 comprises at least one recess ( analogous to that labeled “ packing box ” in fig6 ) in which at least one lateral support assembly 130 ( see fig8 ) may be sealingly positionable along the plunger as part of a tunable plunger seal embodiment . schematic representations of a tunable suction valve 95 ( illustrated for simplicity as a hinged check valve ), a tunable discharge valve 97 ( also illustrated for simplicity as a hinged check valve ), and a piston / plunger 93 ( illustrated for simplicity as a plunger ) are shown in their respective bores . note that longitudinally - moving valve bodies in check valve embodiments schematically illustrated herein ( e . g ., valve body 10 ) are associated with certain operational phenomena analogous to phenomena seen in hinged check valves ( including , e . g ., structural compliance secondary to closing energy impulses ). regarding the graphical aids of fig6 , the double - ended arrows that signify fluid communication between the bores ( suction , discharge and piston / plunger ) and the pumping chamber are double - ended to represent the fluid flow reversals that occur in each bore during each transition between pressure stroke and suction stroke of the piston / plunger . the large single - ended arrow within the pumping chamber is intended to represent the periodic and relatively large , substantially unidirectional fluid flow from suction bore through discharge bore during pump operation . further regarding the graphical aids of fig6 , tunable suction ( check ) valve 95 and tunable discharge ( check ) valve 97 are shown schematically as hinged check valves in fig6 because of the relative complexity of check valve embodiments having longitudinally - moving valve bodies . more detailed schematics of several check valve assemblies and elements are shown in fig1 - 11 , certain tunable check valve embodiments comprising a tunable check valve assembly and a tunable valve seat . in general , the tunable check valve assemblies / tunable radial arrays of tunable suction and discharge valves will typically be tuned to different assembly resonant frequencies because of their different positions in a subassembly housing 78 ( and thus in a pump housing as described herein ). pump housing resonant frequencies that are measured proximate the tunable suction and discharge valves will differ in general , depending on the overall pump housing design . in each case they serve to guide the choices of the respective assembly resonant frequencies for the valves . note that the combination of major components labeled in fig6 as a pump fluid end subassembly 88 is so labeled ( i . e ., is labeled as a subassembly ) because typical fluid end configurations comprise a plurality of such subassemblies combined in a single machined block . thus , in such typical ( multi - subassembly ) pump fluid end designs , as well as in less - common single - subassembly pump fluid end configurations , the housing is simply termed a “ pump housing ” rather than the “ subassembly housing 78 ” terminology of fig6 . further as schematically - illustrated and described herein for clarity , each pump fluid end subassembly 88 comprises only major components : a pumping chamber 74 , with its associated tunable suction valve 95 , tunable discharge valve 97 , and piston / plunger 93 in their respective bores 76 , 72 and 70 of subassembly housing 78 . for greater clarity of description , common fluid end features well - known to those skilled in the art ( such as access bores , plugs , seals , and miscellaneous fixtures ) are not shown . similarly , a common suction manifold through which incoming pumped fluid is distributed to each suction bore 76 , and a common discharge manifold for collecting and combining discharged pumped fluid from each discharge bore 72 , are also well - known to those skilled in the art and thus are not shown . note that the desired check - valve function of tunable check valves 95 and 97 schematically - illustrated in fig6 requires interaction of the respective tunable check valve assemblies ( see , e . g ., fig1 - 5 ) with a corresponding ( schematically - illustrated ) tunable valve seat ( see , e . g ., fig7 , 8 , 10 and 11 ). the schematic illustrations of fig6 are only intended to convey general ideas of relationships and functions of the major components of a pump fluid end subassembly . structural details of the tunable check valve assemblies that are in turn part of tunable check valves 95 and 97 of the invention ( including their respective tunable valve seats ) are illustrated in greater detail in other figures as noted above . such structural details facilitate a plurality of complementary functions that are best understood through reference to fig1 - 5 and 7 - 11 . the above complementary functions of tunable check valves include , but are not limited to , closing energy conversion to heat via structural compliance , energy redistribution through rejection of heat to the pumped fluid and pump housing , vibration damping and / or selective vibration spectrum narrowing through changes in tunable check valve assembly compliance , vibration frequency down - shifting ( via decrease in rebound characteristic frequency ) through increase of rebound cycle time , and selective vibration attenuation through energy dissipation ( i . e ., via redistribution ) at predetermined assembly resonant frequencies . fig7 is a schematic illustration of two views of an exploded partially - sectioned 3 - dimensional view including a check valve body 10 and its convex valve seat interface 22 , together with concave mating surface 24 of tunable valve seat 20 . mating surface 24 is longitudinally spaced apart from a pump housing interface surface 21 . a curved longitudinal section edge 28 of the tunable valve seat &# 39 ; s mating surface 24 , together with a correspondingly greater curved longitudinal section edge 26 of the valve body &# 39 ; s valve seat interface 22 , are shown schematically in detail view a to aid description herein of a rolling valve seal . the correspondingly greater curvature of valve seat interface 22 , as compared to the curvature of mating surface 24 , effectively provides a rolling seal against fluid leakage which reduces wear on the surfaces in contact . the rolling seal also increases longitudinal compliance of a tunable suction or discharge valve of the invention , with the added benefit of increasing the rise and fall times of the closing energy impulse ( thus narrowing the associated vibration spectrum ). widening the closing energy impulse increases rebound cycle time and correspondingly decreases rebound characteristic frequency . further regarding the terms “ correspondingly greater curvature ” or “ correspondingly less curvature ” as used herein , note that the curvatures of the schematically illustrated longitudinal section edges ( i . e ., 26 and 28 ) and the surfaces of which they are a part ( i . e ., valve seat interface 22 and mating surface 24 respectively ) are chosen so that the degree of longitudinal curvature of valve seat interface 22 ( including edge 26 ) exceeds that of ( i . e ., has correspondingly greater curvature than ) mating surface 24 ( including edge 28 ) at any point of rolling contact . in other words , mating surface 24 ( including edge 28 ) has correspondingly less curvature than valve seat interface 22 ( including edge 26 ). hence , rolling contact between valve seat interface 22 and mating surface 24 is always along a substantially circular line , the plane of which is transverse to the ( substantially coaxial ) longitudinal axes of valve body 10 and tunable valve seat 20 . note that although valve seat interface 22 and mating surface 24 ( and other valve seat interface / mating surface combinations described herein ) are schematically illustrated as curved , either may be frusto - conical ( at least in part ) in certain tuned component embodiments . such frusto - conical embodiments may have lower fabrication costs and may exhibit suboptimal down - shifting performance and / or wear characteristics . they may be employed in relatively lower - pressure applications where other tunable component characteristics provide sufficient operational advantages in vibration control . the above discussion of rolling contact applies to the alternate tunable valve seat 20 ′ of fig8 , as it does to the tunable valve seat 20 of fig7 . fig8 schematically illustrates a 3 - dimensional exploded and partially - sectioned view of a tunable valve seat showing a mating surface ( analogous to mating surface 24 of fig7 ) longitudinally spaced apart from a lateral support mounting surface 21 ′. but the lateral support mounting surface 21 ′ in fig8 differs from pump housing interface surface 21 of fig7 in that it facilitates adjustably securing a lateral support assembly 130 to alternate tunable valve seat 20 ′. lateral support assembly 130 comprises first and second securable end spacers ( 110 and 124 respectively ) in combination with a plurality of circular viscoelastic support elements ( 114 , 118 and 122 ), each support element comprising a support circumferential tubular area ( see areas 112 , 116 and 120 respectively ). shear - thickening material in each support circumferential tubular area 112 , 116 and 120 is chosen so each lateral support assembly 130 has at least one predetermined resonant frequency . lateral support assemblies thus configured may be part of each tunable valve seat and each tunable plunger seal . when part of a tunable plunger seal , one or more lateral support assemblies 130 reside in at least one recess analogous to the packing box schematically illustrated adjacent to piston / plunger 93 ( i . e ., as a portion of piston / plunger bore 70 ) in fig6 . note also that in general , a tunable ( suction or discharge ) check valve of the invention may comprise a combination of a tunable check valve assembly 99 ( see , e . g ., fig1 ) and a tunable valve seat 20 ( see , e . g ., fig7 ) or a tunable valve seat 20 ′ ( see , e . g ., fig8 ). referring more specifically to fig6 , tunable suction check valve 95 is distinguished from tunable discharge check valve 97 by one or more factors , including each measured resonant frequency to which each tunable check valve is tuned so as to optimize the overall effectiveness of valve - generated vibration attenuation in the associated pump housing 78 . fig9 - 11 show schematic exploded views of a nonlinear spring - mass damper 227 / 228 / 229 / 230 , which may be incorporated in a tunable check valve assembly embodiment 210 . fig9 - 11 can each be understood as schematically illustrating a tunable check valve assembly with or without a peripheral groove viscoelastic element . that is , each figure may also be understood to additionally comprise a viscoelastic groove element analogous to groove element 54 ( see fig2 ) residing in groove 218 ′/ 218 ″ ( see fig9 )— this groove element is not shown in exploded fig9 - 11 for clarity , but may be considered to comprise at least one circumferential tubular area analogous to tubular area 58 in groove element 54 ( see fig2 ), each tubular area 58 being substantially filled with at least one shear - thickening material 80 chosen to achieve at least one predetermined assembly resonant frequency . referring to fig9 , belleville springs 227 / 228 / 229 are nonlinear , and they couple mass 230 to the valve body base plate 216 and the proximal valve body portion 214 . additionally , dilatant liquid 242 is optionally added ( via sealable ports 222 and / or 220 ) to central internal cavity 224 to immerse nonlinear spring - mass damper 227 / 228 / 229 / 230 . the nonlinear behavior of dilatant liquid 242 in shear ( as , e . g ., between belleville springs 227 and 228 ) expands the range of tuning the nonlinear spring - mass damper 227 / 228 / 229 / 230 to a larger plurality of predetermined frequencies to reduce “ ringing ” of valve body 214 / 216 in response to a closing energy impulse . to clarify the function of nonlinear spring - mass damper 227 / 228 / 229 / 230 , mass 230 is shown perforated centrally to form a washer shape and thus provide a passage for flow of dilatant liquid 242 during longitudinal movement of mass 230 . this passage is analogous to that provided by each of the belleville springs 227 / 228 / 229 by reason of their washer - like shape . fig1 shows an exploded view of an alternate embodiment of a tunable check valve comprising the tunable check valve assembly 210 of fig9 , plus a tunable valve seat 250 . fig1 and 11 schematically illustrate two views of an exploded partially - sectioned 3 - dimensional view including a valve body 214 / 216 and its valve seat interface 234 , together with mating surface 254 of tunable valve seats 250 and 250 ′. mating surface 254 is longitudinally spaced apart from pump housing interface surface 252 in fig1 , and from lateral support mounting surface 252 ′ in fig1 . in fig1 , a curved longitudinal section edge 256 of the tunable valve seat &# 39 ; s mating surface 254 , together with a correspondingly greater curved longitudinal section edge 236 of valve seat interface 234 , are shown schematically to aid description herein of a rolling valve seal . note that valve body 214 / 216 may be fabricated by several methods , including that schematically illustrated in fig9 - 11 . for example , circular boss 215 on proximal valve body portion 214 may be inertia welded or otherwise joined to circular groove 217 on valve body base plate 216 . such joining results in the creation of peripheral seal - retention groove 218 ′/ 218 ″ having proximal groove wall 218 ′ and distal groove wall 218 ″. to enhance scavenging of heat due to friction loss and / or hysteresis loss , liquid polymer ( s ) 242 may be augmented by adding nanoparticles which are generally invisible to the eye as they are typically dispersed in a colloidal suspension . nanoparticles comprise , for example , carbon and / or metallic materials such as copper , beryllium , titanium , nickel , iron , alloys or blends thereof . the term nanoparticle may conveniently be defined as including particles having an average size of up to about 2000 nm . see , e . g ., the &# 39 ; 320 patent . the correspondingly greater curvature of valve seat interface 234 , as compared to the curvature of mating surface 254 , effectively provides a rolling seal against fluid leakage which reduces wear on the surfaces in contact . the rolling seal also increases longitudinal compliance of a tunable suction or discharge valve of the invention , with the added benefit of increasing the rise and fall times of the closing energy impulse ( thus narrowing the associated vibration spectrum ). further regarding the term “ correspondingly greater curvature ” as used herein , note that the curvatures of the schematically illustrated longitudinal section edges ( i . e ., 236 and 256 ) and the surfaces of which they are a part ( i . e ., valve seat interface 234 and mating surface 254 respectively ) are chosen so that the degree of longitudinal curvature of valve seat interface 234 ( including edge 236 ) exceeds that of ( i . e ., has correspondingly greater curvature than ) mating surface 254 ( including edge 256 ) at any point of rolling contact . hence , rolling contact between valve seat interface 234 and mating surface 254 is always along a substantially circular line , the plane of which is transverse to the ( substantially coaxial ) longitudinal axes of valve body 214 / 216 and tunable valve seat 250 . ( see notes above re frusto - conical valve seat interface shapes and mating surfaces ). the above discussion of rolling contact applies to the alternate tunable valve seat 250 ′ of fig1 , as it does to the tunable valve seat 250 of fig1 . but the lateral support mounting surface 252 ′ in tunable check valve 399 of fig1 differs from pump housing interface surface 252 of fig1 in that it facilitates adjustably securing a lateral support assembly 330 to alternate tunable valve seat 250 ′ to form tunable valve seat 389 . lateral support assembly 330 comprises first and second securable end spacers ( 310 and 324 respectively ) in combination with a plurality of circular viscoelastic support elements ( 314 , 318 and 322 ), each support element comprising a support circumferential tubular area ( 312 , 316 and 320 respectively ). note that in general , a tunable ( suction or discharge ) check valve of the invention may comprise a combination of a tunable check valve assembly 210 ( see , e . g ., fig9 ) and a tunable valve seat 250 ( see , e . g ., fig1 ) or a tunable valve seat 250 ′ ( see , e . g ., fig1 ). referring more specifically to fig6 , tunable suction valve 95 is distinguished from tunable discharge check valve 97 by one or more factors , including each measured or estimated resonant frequency to which each tunable check valve is tuned so as to optimize the overall effectiveness of valve - generated vibration attenuation in the associated pump housing 78 .