Abstract: This paper describes an analysis of the fundamental mode of three-dimensional coupled vibrations of composite piezoelectric vibrator by using the apparent elasticity method.
A very simple analytic formula for the resonant frequency of the vibrator is obtained and from that the variations of frequency constant with the geometric size of the vibrator are calculated.
A satisfactory agreement is obtained between our results and the published results which were calculated by using the finite element method. Because the formula is quite simple, the resonant frequency of the vibrator can be quickly calculated by using a scientific calculator, without having to use a computer, and therefore, this method is more convenient than the finite element method for engineering design and estimation.
In addition, a frequency dispersion formula of "longintudinal" wave phase velocity in the finite cylinder is given and a comparison between it and those in the infinite cylinder is made. Finally, it should be obvious that this method may be also used to calculate the resonant frequencies of other composite piezoelectric vibrators.