利用小挠度理论推导设计压电双晶片弯曲振动的频率方程,得到其弯曲振动位移解.利用有限元方法计算压电双晶片弯曲振动的谐振频率.对研制的压电双晶片振子测得其谐振频率,测试结果与有限元计算结果、利用压电方程和小挠度理论推导的频率方程求得的结果相吻合.这说明,所推导的频率方程可于设计自由边界压电双晶片振子. Using the theory of small deflection, the frequency equation of the bending vibration of the piezoelectric bimorph was deduced, and the displacement vibration of the piezoelectric bimorph vibration was obtained.The resonance frequency of the piezoelectric bimorph vibration was calculated by using the finite element method.The resonance of the piezoelectric bimorph vibration was measured Frequency and test results agree well with those calculated by the finite element method and the frequency equations deduced by piezoelectric theory and small deflection theory.This shows that the derived frequency equation can be used to design a free boundary piezoelectric bimorph oscillator.