Transient responses in a two-layered elasto-piezoelectric composite hollow cylinder

The transient responses in a two-layered elasto-piezoelectric composite hollow cylinder in the state of axisymmetric plane strain are obtained. The solution for the charge equation of electrostatics is first expressed by an unknown function with respect to time. Then the governing equations, involving the unknown function of time, for mechanical field are derived. By the method of superposition, both of the dynamic solutions for elastic and piezoelectric layers are divided into two parts as quasi-static and dynamic parts. The quasi-static part is obtained in an explicit form by the state space method and the dynamic part is obtained by the separation of variable method. By virtue of the obtained quasi-static and dynamic parts as well as the electric boundary conditions, a Volterra integral equation of the second kind with respect to the unknown function of time is derived. Interpolation method is introduced successfully to solve the integral equation efficiently. The displacements, stresses and electric potentials are finally obtained. Numerical results are presented at the end.