RLC串联电路与微梁耦合系统1:2内共振分析

Analysis of the 1:2 internal resonance of coupled RLC circuit and microbeam system

研究电阻电感电容串联电路与微梁耦合系统的非线性振动,应用拉格朗日-麦克斯韦方程,建立受静电激励RLC串联电路与微梁耦合系统的数学模型。根据非线性振动的多尺度法,得到了在内共振ω2≈2ω1的情况下的近似解,并进行数值计算,得到用椭圆函数表示的解析解。计算结果表明,在无阻尼情况下,振动和能量在两个态间相互转换,没有能量损失。

In order to study the nonlinear vibration of coupled RLC series circuit and microbeam system subjected to voltage, a mathematical model is established according to the Lagrange-Maxwell equation. Based on the method of multiple scales, the approximation solutions and the numerical calculations are carried out under the conditions of internal resonance ω2≈2ω1 of the system. Analytic solution is obtained by elliptic function. The results show that the energy of vibration exchanges continuously between the two modes.