Thickness vibrations of a piezoelectric plate with dissipation

The three-dimensional (3-D) 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 effects of dissipation on the propagation of plane waves in an infinite solid and forced thickness vibrations in an infinite piezoelectric plate with 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. For the forced thickness vibrations of an infinite plate, the complex coupling factor K*, input admittance Y are derived and an explicit, approximate expression for K* is obtained in terms of material properties. Effects of the viscosity and conductivity on the resonance frequency, modes, admittance, attenuation coefficient, dynamic time constant, coupling factor, and quality factor are calculated and examined for quartz and ceramic barium titanate plates.