MULTI-DIMENSIONAL COUPLED VIBRATIONS OF PIEZOELECTRIC VIBRATORS （I） PURE PIEZOELECTRIC VIBRATORS

In this paper, the fundamental modes of two- and three-dimensional coupled vibrations of various piezoelectric vibrators, including rectangular cross-sectional bar, rectangular plate, solid cylinder and hollow cylinder, are analyzed by using apparent elasticity method. Some quite simple analytic formulae for the resonant frequencies of above-mentioned piezoelectric vibrators are obtained and from those the vibrations of frequency constants with the geometric size of vibrators are calculated.
A satisfactory agreement is obtained between our results and the published experimental. results and theoretical results which were calculated by using other various methode, including the finite diffrerence method, the finite element method and Bitz variational method.
Because these formulae are quite simple, the resonant frequencies of vibrators can be quickly calculated by using scientific calculator, without having to use computer, and thenthis method is more convenient than the other methods above mentioned for engineering design and estimation.
In addition, the errors caused by neglecting piezoelectric effect are discussed in detail for a few kinds of usual piezoelectric material.
Finally, it should be emphasize that this method may be also used to calculate resonant frequencies of composite piezoelectric vibrators.