Dynamic focusing effect and response histories of piezoelectric solid cylinders subjected to impact pressures on the external boundary

A simply analytical method was presented to solve the response histories of dynamic stresses and transient electric potential in piezoelectric solid cylinders subjected to impact pressures on the external boundary.During the course of solving,the electroelastic dynamic equilibrium equation is decomposed into a homogeneous quasi-static equation,which satisfies the inhomogeneous boundary conditions,and an inhomogeneous dynamic equation,which satisfies homogeneous boundary conditions.Utilizing the finite Hankel transform,Laplace transform and their inverse transformation,the analytical expressions of dynamic stresses and transient electric potential in the piezoelectric solid cylinder are obtained.From practical examples,it is found that dynamic focusing effect of dynamic stresses and transient electric potential at the center of piezoelectric solid cylinders are dependent on different piezoelectric materiak.Because electroelastic waves accumulate at the center,and reflect at the external boundary,the dynamic stresses and transient electric potential occur in periodic oscillation.