Vibrations of piezoelectric plates without and with dissipation.

摘要

Exact and closed-form solutions are obtained from three-dimensional equations for free vibrations of an infinite, asymmetric bimorph plate of piezoelectric ceramics. Dispersion curves are calculated for different materials as well as for various thickness ratios. The solutions reduce to those of homogeneous plate as rt = 0 and to those of symmetric bimorph plate as rt = 1. The effects of changes in thickness ratios on the behavior of various frequency branches are examined in details.; Energy dissipation attributed to acoustic viscosity as well as electric current conductivity is investigated for high-frequency vibrations and wave propagation in unbounded solids and along infinite plates of piezoelectric ceramics and various cuts of quartz. Free and piezoelectrically forced thickness-vibrations are studied and the mode shapes of displacements and potentials are obtained. Effects of the viscosity and conductivity on the resonance frequency, modes, attenuation coefficients, time constants and coupling factor are calculated and examined.; In the extended framework incorporating the two aforementioned dissipation factors, solutions of plane harmonic wave of arbitrary direction in an infinite and dissipative piezoelectric plate with general symmetry are obtained. Dispersion curves are computed and plotted for real frequencies and complex wave numbers and are compared with those obtained from the linear 3-D theory without dissipation. Effects of energy loss on the wave propagation are examined in detail for AT-cut of quartz as well as ceramic plate of barium titanate.; Piezoelectric ceramic plate of finite length with a pair of free edges is studied. First, we study a non-dissipative plate with a pair of traction-free and charge-free surfaces. Second, under dissipative assumptions, we study a plate with alternating voltage applied to its two surfaces. The solutions are expanded in series of exact functions obtained from the exact solutions. Frequency spectrums are computed and plotted from solving both the free vibration and forced vibration problems for the non-dissipative model and dissipative model, respectively. Mode shapes at various points of the frequency spectrum, both along the length as well as along the thickness directions, are calculated and explained.