Piezoelectric cylinder under voltage and axial loading

Abstract

This paper considers quasi-static linear response of a solid piezoelectric cylinder due to electric voltage and mechanical loading applied at the ends. A recently developed analytical general solution for an annular cylinder of finite length is used to analyze this complex mixed-boundary value problem. The general solution for electroelastic field and the applied loading are expressed in terms of Fourier-Bessel infinite series. Both flexible electrodes in smooth contact with and rigid electrodes bonded to the cylinder ends are considered. The problem is formulated by dividing the electrode contact area into several annular rings and developing a flexibility equation system based on a set of influence functions to satisfy the mixed-boundary conditions at the cylinder ends. The present approach allows consideration of a cylinder under a variety of electromechanical loading conditions. Accuracy of the present scheme is confirmed by comparing with the existing solutions for the limiting case of an elastic cylinder. Selected numerical results for different cylinder length-radius ratios, electrode dimensions, materials and electric voltage and mechanical loads are presented to demonstrate the coupled electromechanical behavior of a cylinder.