Dynamic Shell Theory for Ferroelectric Ceramics

Abstract

Plates and shells of ferroelectric ceramics are widely used as electromechanical transducers. The theory of piezoelectricity in which the equations of classical elasticity and electrostatics are coupled with linear constitutive relations can be used to predict the behavior of these materials. In this paper, a shell theory is derived by assuming an orthotropic material in which the principal axes of orthotropy coincide with the two principal directions of the reference surface and its normal. The theory reduces to the piezoelectric theory developed by Tiersten and Mindlin for plates [“Forced Vibrations of Piezoelectric Crystal Plates,” Quart. Appl. Math. 20, No. 2, 107–119 (1962)], and to the shear theory of shells for elastic materials. In addition to the usual elastic boundary conditions of shell theory, the electrical quantities of surface potential, surface charge density, or total charge on an equipotential surface may be prescribed. The free vibration of a shell with complete electrodes on both surfaces, either open or short circuited, and a shell without electrodes is discussed. The equations are solved by a numerical integration technique, and some results for a cylindrical shell are presented.