RLC串联电路与微梁耦合系统1:2内共振分析

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。

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

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 ω_2 ≈ 2ω_1 of the system.Analytic solution is obtained by elliptic function.The results show that the energy of vibration exchanges continuously between the two modes.