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中文摘要：
考虑有限变丑，横向的惯性和砍的紧张的有弹性的杆的一个 nonlineax 波浪方程在这篇论文借助于哈密尔顿原则被导出。非线性的波浪方程和截断的非线性的波浪方程被 Jacobielliptic 正弦功能扩大和第三种 Jacobi 椭圆形的功能扩大方法解决。这些非线性的方程的准确周期的答案被获得，包括冲击波答案和独居的波浪答案。准确周期的答案，吃惊答案和独居的答案存在的必要条件被讨论。
英文摘要：
A nonlinear wave equation of elastic rod taking account of finite deformation, transverse inertia and shearing strain is derived by means of the Hamilton principle in this paper. Nonlinear wave equation and truncated nonlinear wave equation are solved by the Jacobi elliptic sine function expansion and the third kind of Jacobi elliptic function expansion method. The exact periodic solutions of these nonlinear equations are obtained, including the shock wave solution and the solitary wave solution. The necessary condition of exact periodic solutions, shock solution and solitary solution existence is discussed.
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