Theory of piezoelectric axisymmetric bimorph

Abstract

A theory of a piezoelectric axisymmetric bimorph is presented in this paper. Bimorphs are often used as electroacoustic transducers, but their use is much wider. A piezoelectic bimorph consists of two or more layers which are placed asymmetrically to the middle surface of the structure. When voltage is supplied to the bimorph, a bending moment is produced which causes transversal deflections of the structure. Average elastic parameters are calculated. Equations for the calculation of bending moments and stretching forces produced by voltage are derived. When the bimorph is a shell of revolution with any shape of meridian, the derived equations can be solved by numerical methods. The finite-element method (FEM) is applied to solve this problem. The bimorph can also be used as a sensor. A theory of such a sensor is also presented. The results obtained by means of the described theory and numerical methods have been verified experimentally or by comparing them with results obtained analytically for a simple structure. It has been proved theoretically that the electric signal produced by a circular transducer clamped on the outer rim of a piezoelectric disc is equal to zero.