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Transient torsional responses of finite piezoelectric hollow cylinder

An exact elastodynamic solution is obtained for torsional vibration of a finite piezoelectric hollow cylinder subjected to dynamic shearing stress and time dependent electric potential at the internal surface. The cylinder is traction free at the two ends and is fixed at the external surface. The piezoelectric material belongs to 622 crystal class. In axial direction, the trigonometric series expansion technique is introduced to guarantee the solution satisfies the end conditions. Then the governing equations for new variables about the radial coordinate r and the time variable t are derived. By means of the normal mode expansion method, the solution for torsional vibration is finally obtained. Numerical investigations are presented and the dynamic behaviors of the finite piezoelectric hollow cylinder are analyzed.