Analyses Of Elastodynamic Response Of FG Cylinders And Thermo-electro-elastic Coupling Of FG Piezoelectric Cylinders

Based on the equation of motion of the axisymmetric plane-strain problem and the stress-displacement relation of elastic materials,an elastodynamic response solution to hollow cylinders with material properties varying in the radial direction is acquired by dividing the cylinder into subshells,with material properties discretized as piecewise constant functions,and using the finite difference scheme in time domain.This paper not only analyzes the effects of the change of material parameter index on the variation of displacement field and stress field along time and radial direction,but also discusses the rationality of the layer number and time step.By employing the continuity of the state vector across all interfaces between the adjacent subshells and the initial and boundary conditions,the state space theory of arbitrarily graded piezoelectric cylinder electro-elastic coupling problem is also established in this paper.Based on the equilibrium equation of the axisymmetric plane-strain problem,the governing equation of electrostatics and the constitutive relation of the electro-elastic coupling problem,a state space solution to piezoelectric hollow cylinder with functionally graded materials is provided by dividing the piezoelectric cylinder into subshells to discretize the material parameters.The influence of the change of material parameter index on radial displacement,radial stress,radial potential shift and radial distribution of potential along radial direction is analyzed.The distributions of the electroelastic field of piezoelectric cylinder under axially symmetric mechanical loads and potential loads are given,respectively.On the basis of the electro-elastic coupling problem,due to the heat conduction equation in one-dimensional steady state,the equilibrium equation,the electrostatic control equation and the constitutive relationship of the thermo-electro-elastic coupling problem,with introducing the heat flux,a state space theory for the thermo-electro-elastic coupling problem of arbitrarily graded piezoelectric cylinder is also established in this paper.The radial distributions of temperature field and electroelastic field of functionally graded piezoelectric cylinder under temperature and multi-field coupling loads are provided.The influence of inhomogeneity of material parameters on the state variables of the system is analyzed.The present solution may not only apply to arbitrarily graded elastic hollow cylinders and piezoelectric hollow cylinders,but also readily satisfy a variety of initial conditions and boundary conditions.According to the numerical analyses for the gradedcylinders and the graded piezoelectric cylinders with material properties varying as a continuous function and a piecewise function,the correctness and validity of the present solution are verified.