用精确电场法和等效电路法计算压电双晶片梁的等效电容

Equivalent capacitance of piezoelectric bimorph beam calculated by precise electric field and equivalent electric circuit methods

采用5端口等效电路法描述压电双晶片梁的动力学特性,通过控制方程和边界条件设计出等效电路,并给出了3种边界情况下的导纳公式,由导纳公式得到等效电容。分别用精确电场法与等电场法计算了压电双晶片梁的等效电容,并进行对比,得到了等效电容在基频附近的变化规律:等电场法高估了共振频率处的等效电容,并低估了共振频率;频率小于基频时,等效电容大于静态电容;频率在基频处,等效电容迅速增大,最大值可达静态电容的10倍;然后等效电容迅速减小,在反共振频率处达到一个小于静态电容的极小值,最后随频率增大而缓慢增大。本研究结果可用于预测压电声子晶体的LC局域共振带隙。

To depict the dynamic behavior of piezoelectric bimorph beam, a five-port equivalent electric circuit model was estab- lished by governing equations and boundary conditions. Admittance formulae for three kinds of mechanical boundary conditions were given. The equivalent capacitances were further derived from these admittance formulae. The variation tendency of equiva- lent capacitance around fundamental frequency was analyzed. These results with precise electric field method （PEFM） were com- pared with those done by equivalent electric field method （EEFM）. The equivalent capacitances around resonance frequencies are overestimated, while resonance frequencies are underestimated by EEFM. Equivalent capacitances are larger than static ones when the driving frequency is less than fundamental frequency. However, when the driving frequency is close to fundamental fre- quency, equivalent capacitances increase dramatically, and reach their maxima at fundamental frequencies, which are over 10 times than static capacitances. Then these equivalent capacitances lessen rapidly with increasing of driving frequency, and achieve minimums at anti-resonance frequencies. Finally, these capacitances increase slowly along with the driving frequency. This re- search can be used to predict the LC locally resonant band gaps of piezoelectric phononic crystal.