## 留言板

 引用本文: 张善元, 刘志芳. 有限变形弹性杆中三种非线性弥散波[J]. 应用数学和力学, 2008, 29(7): 825-832.
ZHANG Shan-yuan, LIU Zhi-fang. Three Kinds of Nonlinear-Dispersive Waves in Finite Deformation Elastic Rods[J]. Applied Mathematics and Mechanics, 2008, 29(7): 825-832.
 Citation: ZHANG Shan-yuan, LIU Zhi-fang. Three Kinds of Nonlinear-Dispersive Waves in Finite Deformation Elastic Rods[J]. Applied Mathematics and Mechanics, 2008, 29(7): 825-832.

## 有限变形弹性杆中三种非线性弥散波

###### 作者简介:张善元(1942- ),男,山西省翼城人,教授,博士生导师(联系人:Tel:+86-351-6010918;E-mail:syzhang@tyut.edu.cn).
• 中图分类号: O347.4

## Three Kinds of Nonlinear-Dispersive Waves in Finite Deformation Elastic Rods

• 摘要: 在一维弹性细杆拉压、扭转和弯曲波的经典线性理论基础上，分别计入有限变形和弥散效应，借助Hamilton变分原理，由统一的方法导出了3种非线性弥散波的演化方程．对3种演化方程进行了定性分析．结果表明，这些方程在相平面上存在同宿轨道或异宿轨道，分别相应于孤波解或冲击波解．根据齐次平衡原理，用Jacobi椭圆函数展开对这些演化方程进行了求解，在一定的条件下它们均可能存在孤立波解或冲击波解，这与方程的定性分析完全一致．
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##### 出版历程
• 收稿日期:  2007-07-24
• 修回日期:  2008-05-22
• 刊出日期:  2008-07-15

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