单壁碳纳米管受电压激励非线性振动研究

RESEARCH ON NONLINEAR VIBRATION FOR ELECTRICALLY ACTUATED SINGLE-WALLED CARBON NANOTUBE

选单壁碳纳米管为研究对象,研究单壁碳纳米管受电压激励非线性问题。碳纳米管两端固定与固定电极板对应,在外部电压激励下,组成一个电容器,根据梁理论建立碳纳米管系统的非线性动力学方程,此方程是一个非线性偏微分方程。应用多尺度法求得系统幅频响应方程,并进行了数值计算,分析了不同的参数对共振的影响。随着碳纳米管长度和交流电压的增加,不稳定区间逐渐增大,振幅增加;随着碳纳米管半径和极板距离的增大,不稳定区间逐渐减小,振幅减小,但当σ接近零时,振幅几乎不随系统参数变化而变化。

This paper presents an investigation of the nonlinear problem of electrically actuated single-walled carbon nanotube. A clamped-clamped carbon nanotube connected to the fixed electrode plate,forming a capacitor under the external excitation voltage. According to the beam theory,the nonlinear dynamic equation of carbon nanotube system is established,it is a nonlinear partial differential equation. By means of the method of multiple scales,nonlinear vibration equation of the system is acquired and the numerical calculation is carried out. Numerical analysis of the influence of different parameters is analyzed.With the increase of carbon nanotube length and AC voltage,the amplitude and the unstable interval become larger. With the increase of carbon nanotube radius and plate distance,the amplitude and the unstable interval become smaller. Whenσis close to zero,the amplitude of the response curves hardly changes with the other system parameters.