Resonant flexural vibrations and dissipative heating of a piezoceramic ring plate with nonuniformly electroded surfaces

Abstract

The forced flexural vibrations and dissipative heating of a bimorph ring plate are studied. The plate is made of viscoelastic piezoceramics and is polarized across the thickness. The outer surfaces of the plate are nonuniformly electroded, and harmonic electric excitation is applied to the electrodes. The viscoelastic behavior of the material is described using the concept of temperature-dependent complex moduli. The coupled nonlinear problem of thermoviscoelasticity is solved by time iteration using, at each iteration, the discrete-orthogonalization method to integrate the mechanics equations and the explicit finite-difference method to solve the heat-conduction equation with a nonlinear heat source. Numerical calculations demonstrate that by changing the size of the ring electrode we can influence the natural frequency, stress and displacement distributions, dissipative-heating temperature, and amplitude-and temperature-frequency characteristics. With certain boundary conditions, there is an optimal electrode configuration that produces deflections of maximum amplitudes when an electric excitation is applied