The Nonlinear Vibration And Buckling Of Shell-type Piezoelectric Nanostructure

Due to the outstanding mechanical,electrical and physical properties,piezoelectric cylindrical nano-shells receive extensive applications in sensors,filters and energy harvesters.Different from the macroscopic piezoelectric structures,piezoelectric cylindrical nano-shell has a larger ratio of surface phase to bulk part,which makes surface/interface effect on the dynamic and static responses of nanostructures significant.In this dissertation,based on the electro-elastic surface/interface theory,the effect of surface/interface on the dynamic and static behaviors of piezoelectric cylindrical nano-shell is studied systematically through detailed methods.The main research contents are as follows:Based on the electro-elastic surface/interface theory together with von Kármán geometric nonlinearity,the free vibration analysis of orthotropic piezoelectric cylindrical nano-shell is investigated.The nonlinear governing differential equations,including surface effect,are established by using Hamilton's principle,and the analytical solutions of nonlinear equations are obtained by means of the homotopy perturbation method.The numerical results indicate that the effect of surface elastic constants on the nonlinear frequency of orthotropic piezoelectric cylindrical nano-shell is consistent with that of surface piezoelectric constants but opposite to that of surface dielectric constants.The forced vibration analysis of functionally graded cylindrical nano-shell covered with a piezoelectric layer is studied by using the Donnell's nonlinear shallow-shell theory as well as electro-elastic surface/interface model.The frequencies and corresponding modes of nano-shell are firstly achieved through linear analysis,and then the nonlinear governing differential equations are established by using Lagrange equations.After that,the relationship between the amplitude and the frequency is presented by means of the Runge-Kutta method.The results show that the effect of surface energy on the relationship between the amplitude and the frequency of nano-shell is significantly important.The buckling and postbuckling behaviors of functionally graded piezoelectric cylindrical nano-shell subjected to uniform lateral pressure are studied.Combined with the electro-elastic surface/interface theory,principle of minimum potential energy and von Kármán geometric nonlinearity,the nonlinear governing differential equations of functionally graded piezoelectric nano-shell are achieved.The asymptotic solutions of buckling torque and postbuckling torque are obtained by using the singular perturbation method.The results show that the buckling load and postbuckling load of the nano-shell are enhanced with the consideration of surface elasticity or surface piezoelectricity,but the inverse case can be found for residual surface stress or surface dielectricity.