Electromechanical coupling factors and fundamental material constants of thickness vibrating piezoelectric plates

Abstract

The vibrations of piezoelectric plates are governed by the linear piezoelectric equations which may contain a rather large number of elastic, piezoelectric and dielectric constants. But under certain very restrictive but practically important circumstances, piezoelectric coupling coefficients occur naturally in the solutions of the equations, a different coefficient arising in each particular case. Under more general circumstances many of the material constants remain in the solution, and the utility or significance of any of the coupling coefficients appears questionable. The solution of the problem of the thickness vibrations of an arbitrarily anisotropic plate is used in demonstrating the significance and limitations of the coupling coefficient for various types of anisotropy. In many of the instances when the coupling coefficient turns out to be useful, the frequency equation shows that the overtone resonances are not integral multiples of the fundamental. The departure from an integral multiple relationship depends on the coupling coefficient only, and consequently, the coupling coefficient can be determined from simple resonance measurements.