MULTIDIMENSIONAL COUPLED VIBRATIONS OF PIEZOELECTRIC VIBRATORS——PURE PIEZOELECTRIC VIBRATORS

In this paper,the fundamental modes of two- and three-dimensional coupled vibrations ofvarious piezoelectric ceramic vibrators,including the rectangular cross-sectional bar,the rectangularplate,the finite solid cylinder and hollow cylinder,are analyzed by using the apparent elasticitymethod,and some quite simple analytic formulae for the resonant frequencies of the above-men-tioned various piezoelectric vibrators are obtained,These formulae have been used to calculatethe variations of frequency constants with the geometric size of the vibrators,and the calculatedresults are in satisfactory agreement with the published experimental results and results calculatedby using various other methods,including the finite difference method,finite element method andRitz 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 acomputer,so this method is more convenient for engineering