Flexural Vibrations of Bilaminar Ceramic Plates

Abstract

The differential equation and boundary conditions that govern the electrically forced flexural vibrations bilaminar ceramic plates are developed from linear piezoelectric equations of state. A general formula for the electrical-input admittance of a bilaminar plate is given. The differential equation can be cast in the classical form for thin plates by defining a “modified flexural rigidity” and a “modified ratio.” The applied voltage does not appear in the differential equation as a forcing term; instead, it enters the problem through the boundary conditions as a uniform applied bending moment at any nonclamped edge of the plate. The effects electromechanical coupling are illustrated by solving the equation in the case of a free-edge disk. The resonance frequencies (for constant applied current) and the vibration patterns at these frequencies vary with electromechanical coupling; hence, the coupling coefficient of the plate material can be inferred from simple careful measurements of resonance frequencies. The effects of rotary inertia and shear on the properties of these plates are indicated. [Work supported in part by U. S. Office of Naval Research.]