碳纳米梁受电压激励的非线性振动分析

An Analysis of Nonlinear Vibration of Electrically Actuated Carbon Nanobeam

选取电荷、广义位移为电路耦合机电系统的广义坐标,得到系统的动能、势能、电能及耗散函数。根据经典的拉格朗日-麦克斯韦方程建立数学模型,得到的振动方程是弱非线性Duffing方程。应用多尺度法求得系统的主共振的幅频响应方程,并进行了数值计算,分析了不同的参数对共振的影响。随着碳纳米梁长度和交流电压幅值的增大,振幅和共振区增大;随着碳纳米梁与固定极板间距和阻尼系数的增大,振幅和共振区减小。

Changing charge and generalized displacement as generalized coordinates of circuit coupling electromechanical system, kinetic energy, potential energy, electrical energy and dissipation function are obtained of a circuit coupling electromechanical system. According to Lagrange function, the weak nonlinear dynamic equation of carbon nanobeam system is established. By means of the multiple scale method of nonlinear vibration of primary resonance of the system are acquired and numerical calculation is carried out. Numerical analysis of the influence of different parameter is analyzed. With the increase of the length of the carbon nanobeam and ac voltage, the amplitude of the response curves and the resonance region enlarge; With the increase of the damping coefficient of the carbon nanobeam and spacing of the nanobeam and fixed plate, the amplitude of the response curves and the resonance region decrease.