基于非局部梁理论的嵌入式弯曲碳纳米管在移动载荷作用下的振动分析

基于非局部连续介质力学理论，针对嵌入式弯曲碳纳米管建立了两端简支的Euler-Bernoulli梁计算模型，研究碳纳米管在移动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，分析了非局部参数因子，纳米管长径比，移动载荷速度，弯曲波纹幅值，弹性介质常数对碳纳米管振动特性的影响，结果表明上述因素对碳纳米管动力特性有很重要影响．

Vibration analysis of embedded curved carbon nanotube subjected to a moving harmonic load based on nonlocal theory

In the present study, forced vibration of a simply supported embedded curved single-walled carbon nanotube （ECSWCNT） subjected to a moving harmonic load is investigated based on nonlocal Euler-Bernoulli beam theory. 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 effects of nonlocal parameter, aspect ratio of ECSWCNT, velocity and the elastic medium constant is discussed. The results show that the above mentioned effects play an important role on the dynamic behavior of ECSWCNT.