Thickness vibrations of piezoelectric plates with dissipation

The three-dimensional equations of linear piezoelectricity with quasi-electrostatic approximation are extended to include losses attributed to the acoustic viscosity and electrical conductivity. These equations are used to investigate the forced thickness vibrations by the thickness excitation in an infinite piezoelectric plate with the most general symmetry. For a harmonic plane wave propagating in an arbitrary direction in an unbounded solid, the complex eigenvalue problem is solved from which the effective elastic stiffness, viscosity, and conductivity are computed from the corresponding frequency-dependent eigenvalues. For the forced thickness vibrations in an infinite plate, the input admittances are obtained and the complex coupling factors are deduced in terms of material properties. Effects of the viscosity and conductivity on the resonance frequencies, modes, attenuation coefficients, time constants and coupling factors are calculated and examined for quartz and ceramic barium titanate plates.