Stress analysis of piezoceramic cylinders

Abstract

The development of versatile analytical methods for analysis of smart structural elements is becoming increasingly important. Solid and thick cylinders are among the most common forms of structural elements used in practical applications. In this paper, the coupled electroelastic equations governing the axisymmetric elastic and electric fields of a long annular piezoceramic cylinder are solved by applying Fourier integral transforms. The ceramic is assumed to be hexagonally symmetric about or polarized along the axis of the cylinder. Explicit analytical solutions are presented for all of the components of the elastic and electric fields. Solutions for a solid cylinder subjected to a radial ring load and a ring electric charge are presented. Solutions for a band load and an electric charge are also presented, and the singularities of the coupled electroelastic fields are examined. Selected numerical solutions for cylinders made out of three different piezoceramics and subjected to a load and an electric charge are presented to demonstrate the salient features of the coupled fields. The general solutions presented in this paper are very useful in the study of load-transfer mechanisms, active regions, and the micromechanics of cylindrical fibre-reinforced composite elements containing piezoceramic sensors/actuators. The present solutions can also be used in the boundary element analysis of cylindrical smart elements.