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| Magnus method for dynamic behavior of embedded single-walled carbon nanotube under harmonic excitation |
| Received:September 25, 2011 Revised:December 25, 2011 |
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| DOI：10.7511/jslx20122002 |
| KeyWord:embedded single-walled carbon nanotube nonlinear oscillations dynamic system magnus expansion geometric integration |
| Author | Institution |
| 王博 |
西北工业大学 力学与土木建筑学院, 西安 |
| 邓子辰 |
西北工业大学 力学与土木建筑学院, 西安 ; 大连理工大学 工业装备结构分析国家重点实验室, 大连 |
| 徐晓建 |
西北工业大学 力学与土木建筑学院, 西安 |
| 王艳 |
西北工业大学 力学与土木建筑学院, 西安 |
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| Abstract: |
| 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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