| 王博,邓子辰,徐晓建,王艳.简谐载荷下嵌入式单壁碳纳米管动态响应的Magnus方法[J].计算力学学报,2012,29(2):159~164 |
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| 简谐载荷下嵌入式单壁碳纳米管动态响应的Magnus方法 |
| Magnus method for dynamic behavior of embedded single-walled carbon nanotube under harmonic excitation |
| 投稿时间：2011-09-25 修订日期：2011-12-25 |
| DOI：10.7511/jslx20122002 |
| 中文关键词: 嵌入式单壁碳纳米管 非线性振动 动力学系统 Magnus级数方法 几何积分 |
| 英文关键词:embedded single-walled carbon nanotube nonlinear oscillations dynamic system magnus expansion geometric integration |
| 基金项目:国家基础研究计划973(2011CB610300);国家自然 科学基金(10972182,11172239,10902089);高校 博士点基金(20106102110019);大连理工大学工业装备结构分析国家重点实验室开放基金(GZ0802); 国家111引智计划(B07050)资助项目. |
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| 中文摘要: |
| 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。 |
| 英文摘要: |
| 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. |
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