RLC串联电路与微梁耦合系统的吸合电压与电振荡

Pull-in voltage and electric oscillations of RLC series circuit and micro-beam coupled system

根据电阻电感电容RLC电路与微梁耦合系统物理模型,利用拉格朗日-麦克斯韦方程建立了反映RLC电路与微梁机电耦合特征的数学模型。此模型能够反映机电的耦合特征。当两个极板之间的电介质为石蜡、陶瓷、云母等填充物时,只需求解RLC串联电路方程;当电路中放电结束瞬间,电容器极板上电荷为零,此时系统转化为极板微梁振动系统。通过伽辽金方法推导出了极板微梁系统的非线性振动方程,并求得了极板的吸合电压;应用常微分方程理论得到了RLC串联电路方程电振荡的解析表达式,分析了系统的电振荡特性。研究结果表明:对于每一个激励电压值,极板都有两个可能的平衡位置;电路中电流在非共振情况下经过一段时间的振荡后达到稳定。

The physical model of resistance,inductance and condenser RLC circuit and micro-beam coupled system is presented.According to the Largrange-Maxwell's equation,the mathematical model of the RLC circuit and micro-beam coupled system is established.The model reflects the characteristics of electromechanical coupling.When the dielectric is ceramic,paraffin or mica,only RLC series circuit equation needs to be solved.At the instant end of discharge,the electric charge on the plates is zero.The system becomes the micro-beam vibration system.According to the Galerkin's method,the vibration equation of the micro-beam system is dirived and Pull-in voltage is obtained.By means of the ordinary differential theory,analytical expression of electric oscillation of the RLC series circuit equation is obtained.Electric oscillations of the system are analyzed.The results show that: For each excitation voltage value the plate has two possible equilibrium positions.After a period of oscillation with non-resonance case the circuit current will reaches to its steady state.