MULTIDIMENSIONAL COUPLED VIBRATIONS OF PIEZOELECTRIC VIBRATORS——COMPOSITE PIEZOELECTRIC VIBRATORS

This paper presents an analysis of the three-dimensional coupled vibrations of a compositepiezoelectric vibrator by using the apparent elasticity method. A very simple analytic formula for the resonant frequency of the vibrator is obtained and withit the variation of the frequency constant with the geometric size of the vibrator is calculated. A satisfactory agreement is obtained as compared with the published results calculated by thefinite element method. Because the formula is quite simple the resonant frequency of the vibrator can be quickly cal-culated by using a scientific calculator,without having to use a computer,and so this method ismore convenient than the finite element method for engineeing design and estirmation. In addition,a dispersion relation of the phase velocity of "longitudinal"waves in the finiteisotropic solid cylinder is given and a comparison between this relation and those in an infinitecylinder is made. This method may also be used to calculate the resonant frequencies of other