Vibration Characteristics Analysis Of Nano-Components And Nano-Reinforced Composites

The vibration characteristics analysis of nano-components and nano-reinforced composites is a hot topic in the mechanical properties of nano-materials.Utilizing the nonlocal theory the scale effect of the nano-components and nano-reinforcements,the dynamic governing equations of the nano-component beams and the macro carbon nanotubes reinforced composites(CNTRCs)beams/plates/shells resting on the visco-Pasternak medium were established.Afterward,the dynamic characteristic parameters of the typical nano-components and nano-reinforced composites under corresponding boundary conditions were obtained.At last,the effects of the scale effect of nano-materials,flexoelectric(FE)effect,visco-Pasternak medium,volume fractions and distribution pattern of carbon nanotubes(CNTs),and size of the structures on the dynamic characteristics of the classic nano-components and nano-reinforced composites were analyzed.The main work and conclusions are summarized as follows:The dynamic characteristics analysis of the nano-component beams resting on the visco-Pasternak medium was carried out.Taking the scale effect,FE effect,and shear deformation of the piezoelectric nano-components into consideration,the dynamic governing equations of the nano-beams on the visco-Pasternak medium were derived based on the Timoshenko beam hypothesis.The semi-analytical solutions of the dynamic characteristic parameters of the simply supported nano-beams were obtained.Moreover,the effects of the scale effect,FE effect,aspect ratio of the nano-beam,and visco-Pasternak medium on the dynamic characteristics of the nano-beams were analyzed.The results show that: the equivalent stiffness of the nano-beams can be weakened by the scale effect and tangential FE coefficient,while the equivalent stiffness of the nano-beams can be increased by the transverse FE coefficient.The dynamic characteristics of the nano-component beams with variable cross-sections resting on the visco-Pasternak medium were analyzed.Further considering the variable cross-section characteristics of the piezoelectric nano-components,the theoretical model of the dynamic characteristics analysis of the nano-beams with variable cross-sections resting on the visco-Pasternak medium was obtained based on the analysis model of the uniform cross section nano-beams.The approximate solutions of the dynamic characteristic parameters of the nano-beams with variable cross-sections under typical boundary conditions were obtained by the perturbed transfer function method.The effects of the scale effect,variable cross-section coefficient,FE effect,and visco-Pasternak medium on the dynamic characteristics of the nano-beams with variable cross-sections were analyzed,it is found that: the impact amplitude of the scale effect on the dynamic characteristic parameters of the nano-beams with variable cross-sections decreases with the increase of the taper coefficient.Besides,the critical damping parameter of the visco-Pasternak medium can be reduced by increasing the taper coefficient.The dynamic characteristics of the macro straight,aligned CNTRCs beams were studied.The nonlocal Eshelby-Mori-Tanaka(EMT)constitutive model of the macro straight,aligned CNTRCs was established by applying the nonlocal theory to consider the scale effect of CNTs.On this basis,the dynamic governing equations of the CNTRCs Timoshenko beams resting on the visco-Pasternak foundation were derived.Afterward,the semi-analytical solutions of the dynamic characteristic parameters of the simply supported CNTRCs beams were obtained.A parametric study was carried out to examine the effects of the scale effect,volume fractions of CNTs,aspect ratio of the beam,and visco-Pasternak foundation on the dynamic characteristics of the CNTRCs beams.The results show that: the inclusion of CNTs can significantly enhance the equivalent structural stiffness of the CNTRCs beams while considering the scale effect of CNTs will reduce the equivalent structural stiffness of the beams.The dynamic characteristics of the macro random-oriented functionally graded(FG-)CNTRCs plates were investigated.Firstly,the nonlocal EMT constitutive model of the macro random-oriented CNTRCs was obtained by considering the scale effect of CNTs.Further considering the influence of the change of the volume fractions of CNTs along the direction of the plate thickness,the change of ambient temperature,and viscoelastic foundation,the dynamic governing equations of the FG-CNTRCs plates resting on the visco-Pasternak foundation in a thermal environment were established based on the Kirchhoff plate theory.The analytical solutions of the dynamic characteristic parameters of the four-side simply supported FG-CNTRCs plates were given.Analysis of the effects of the scale effect,volume fractions and distribution type of CNTs,sizes of the plate,change of the environment temperature,and visco-Pasternak foundation on the dynamic characteristics of the FG-CNTRCs plates was carried out.The results show that: the equivalent stiffness of the FG-CNTRCs plates can be reduced by considering the scale effect of CNTs and the change of ambient temperature.The dynamic characteristics analysis of the macro random-oriented FG-CNTRCs cylindrical shells was carried out.Based on the nonlocal EMT constitutive model of the macro random-oriented CNTRCs and the Kirchhoff-Love cylindrical shell theory,and considering the effects of the change of the volume fractions of CNTs along the direction of the shell thickness,the change of environment temperature,and viscoelastic foundation,the free vibration governing equations of the FG-CNTRCs cylindrical shells resting on the visco-Pasternak foundation in a thermal environment were established.The semi-analytical solutions of the dynamic characteristic parameters of the simply supported FG-CNTRCs shell were obtained.By analyzing the effects of the scale effect,volume fractions and distribution pattern of CNTs,sizes of the cylindrical shell,change of the environment temperature,and visco-Pasternak foundation on the dynamic characteristics of the FG-CNTRCs cylindrical shells,it is found that: the dynamic characteristic parameters of the structure are greatly affected by the size parameter L/h.In conclusion,the theoretical models for the dynamic characteristics analysis of the typical nano-components and nano-reinforced composites were established based on the nonlocal theory in this study.The related results can provide theoretical guidance for the development and application in the engineering of nano-components and nano-reinforced composites.