Traction-free vibration of layered elastic and piezoelectric rectangular parallelepipeds

A variational method is developed to study the traction-free vibration of layered rectangular elastic and piezoelectric parallelepipeds. The weak form of the equations of motion and the charge equation are formulated in rectangular Cartesian coordinates. Approximate solutions to these equations are sought in a form that combines piecewise linear or quadratic Lagrange basis functions through the layered dimension of the solid with continuous global polynomial or trigonometric functions in the plane. This allows for the necessary discontinuity in the shear strain and normal potential gradient across the interface between layers caused by the mismatch in material properties. Numerical results compare very well with those computed by other techniques for layered elastic and piezoelectric plates with simple support and homogeneous parallelepipeds under stress-free conditions.