MULTI-DIMENSIONAL COUPLED VIBRATIONS OF PIEZOELECTRIC VIBRATORS II COMPOSITE PIEZOELECTRIC VIBRATORS

In this paper, the fundamental modes of two- and three-dimensional coupled vibrations of various piezoelectric ceramic vibrators, including the rectangular cross-sectional bar, the rectangular plate, the finite solid cylinder and hollow cylinder, are analyzed by using the apparent elasticity method, and some quite simple analytic formulae for the resonant frequencies of the above-mentioned various piezoelectric vibrators are obtained These formulae have been used to calculate the variations of frequency constants with the geometric size of the vibrators, and the calculated results are in satisfactory agreement with the published experimental results and results calculated by using various other methods, including the finite difference method, finite element method and Ritz variational method. These formulae are quite simple, and the resonant frequencies or the geo-metric size of the vibrators can be rapidly calculated by using a scientific calculator instead of a computer, so this method is more convenient for engineering design and estimation than the various method mentioned above. In addition, for a few kinds of usual piezoelectric ceramic materials, the errors caused by neglecting the piezoelectric effect are discussed in detail. Finally, it should be pointed out that this method can be also used to calculate the resonant frequencies of composite piezoelectric vibrators.