Plane harmonic waves in an infinite piezoelectric plate with dissipation.

In a previous paper, the three-dimensional equations of linear piezoelectricity with quasielectrostatic approximation were extended to include losses attributed to the mechanical damping in solid and the resistance in current conduction. These equations were used to investigate the plane wave propagation in an unbounded solid and forced thickness vibration of an infinite piezoelectric plate. In the present paper, these equations are used to obtain solutions of plane harmonic wave of arbitrary direction in an infinite and dissipative piezoelectric plate with general crystal symmetry. Dispersion curves are computed and plotted for real frequencies and complex wave numbers. All frequency branches are complex for dissipative plate. There are no longer any pure real or pure imaginary or complex conjugate frequency branches as those existing for nondissipative plates. Effects of dissipation on the wave propagation are examined in detail for AT-cut of quartz as well as barium titanate ceramic plate.