压电振子的多维耦合振动（Ⅱ）——复合压电振子

本文利用表观弹性法分析了复合压电振子的三维耦合振动的基频本振方式,得到了振子共振频率的很简单的解析表达式并由此计算了频率常数随振子尺寸变化的关系曲线。本文的计算结果同已发表的用有限元法计算的结果满意地符合。由于计算公式十分简单,因此共振频率的计算可以用微型计算器很快计算出来而无需用电子计算机,所以这种方法对工程设计和估算来说要比有限元法简便得多。
此外,还给出了有限长圆柱中“纵波”相速的频散公式,并与无限长圆柱中的公式进行了比较。
本方法也可用来计算其它复合压电振子的共振频率。

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

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