简谐载荷下嵌入式单壁碳纳米管动态响应的Magnus方法

基于两端固支的弹性梁模型,研究嵌入式单壁碳纳米管在横向简谐载荷作用下的非线性振动问题。利用Galerkin方法对运动微分方程进行近似处理,将原方程从非线性动力学系统转化到二阶动力学系统,对于二阶动力学方程采用Magnus级数方法进行求解。通过数值实验,分析了嵌入式单壁碳纳米管非线性振动幅频特性,根据非线性动力学理论分析了碳纳米管动态响应,结果表明倍周期分岔产生混沌。

Magnus method for dynamic behavior of embedded single-walled carbon nanotube under harmonic excitation

Based on the continuum mechanics and elastic beam model,the nonlinear vibration of embedded single-walled carbon nanotube with clamped-clamped boundary condition is investigated,where the carbon nanotube is modeled as a harmonically excited beam under a transverse force.By using a single-mode Galerkin approximation method,the nonlinear integral-differential equation governing the motion of the nanotube is converted into a second-order nonlinear ordinary differential equation.The differential equation of the model is solved using Magnus expansion method which is one of the geometric integration methods.In the numerical calculation,the amplitude-frequency response curves for embedded single-walled carbon nanotube are analyzed,the effects of the surrounding elastic medium on the amplitude-frequency response characteristics are discussed,the periodic orbits and their bifurcations are obtained,the nonlinear dynamic theory shows that a sequence of period-doubling bifurcations leading to chaos.