Piezoelectric study on circularly cylindrical layered media

Abstract

In this paper, an analytical solution in series form for the problem of a circularly cylindrical layered piezoelectric composite consisting of N dissimilar layers is presented within the framework of linear piezoelectricity. Each layer of the composite is assumed to be transversely isotropic with respect to the longitudinal direction ( x 3 direction), and the composite is subject to arbitrary electromechanical singularities infinitely extended in a direction perpendicular to the x 1– x 2 plane such that only in-plane electric fields and out-of-plane displacement are produced. The alternating technique in conjunction with the method of analytical continuation is applied to derive the general multilayered media solution in an explicit series form, whose convergence is guaranteed numerically. The distributions of the shear stress and electric field are found to be dependent on the material combinations and the magnitude and position of the electromechanical singularities. An exactly closed form solution is obtained and discussed graphically for a practical example.