| 有限变形弹性圆杆中的孤波 |
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| 引用本文： | 刘志芳,张善元.有限变形弹性圆杆中的孤波[J].应用数学和力学,2006,27(10):1255-1260. |
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| 作者姓名： | 刘志芳 张善元 |
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| 作者单位： | 太原理工大学 应用力学研究所,太原 030024 |
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| 基金项目： | 国家自然科学基金;山西省自然科学基金 |
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| 摘 要： | 在同时引入横向惯性和横向剪切应变的情况下，导出了有限变形弹性圆杆的非线性纵向波动方程，方程中包含了二次和三次的非线性项以及由横向剪切与横向惯性导致的两种几何弥散效应．借助Mathematica软件，利用双曲正割函数的有限展开法，对该方程和对应的截断的非线性方程进行求解，得到了非线性波动方程的孤波解，同时给出了这些解存在的必要条件．
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| 关 键 词： | 非线性波 有限变形 横向惯性 横向剪切应变 双曲正割函数 |
| 文章编号： | 1000-0887（2006）10-1255-06 |
| 收稿时间： | 2005-03-15 |
| 修稿时间： | 2006-05-01 |
Solitary Waves in Finite Deformation Elastic Circular Rod |
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| LIU Zhi-fang,ZHANG Shan-yuan.Solitary Waves in Finite Deformation Elastic Circular Rod[J].Applied Mathematics and Mechanics,2006,27(10):1255-1260. |
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| Authors: | LIU Zhi-fang ZHANG Shan-yuan |
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| Institution: | Institute of Applied Mechanics, Taiyuan University of Technology, Taiyuan 030024, P. R. China |
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| Abstract: | A new nonlinear wave equation of a finite deformation elastic circular rod simultaneously introducing transverse inertia and shearing strain was derived by means of Hamilton principle. The nonlinear equation includes two nonlinear terms caused by finite deformation and double geometric dispersion effects caused by transverse inertia and transverse shearing strain. Nonlinear wave equation and corresponding truncated nonlinear wave equation were solved by the hyperbolic secant function finite expansion method. The solitary wave solutions of these nonlinear equations are obtained. The necessary condition of these solutions existence is given also. |
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| Keywords: | nonlinear wave finite deformation transverse inertia transverse shearing strain hyperbolic secant function |
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