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中文摘要：
利用Hamilton变分原理，导出了计及有限变形和横向Possion效应的弹性杆中非线性纵向波动方程．利用Jacobi椭圆正弦函数展开和第三类Jacobi椭圆函数展开法，对该方程和截断的非线性方程进行求解，得到了非线性波动方程的两类准确周期解及相应的孤波解和冲击波解，讨论了这些解存在的必要条件．
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 Hamihon principle. 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 expan- sion method. The exact periodic solutions of these nonlinear equations are obtained, including the shock wave solution and the solitary wave solution. The necessary condition for the existence of exact periodic solutions, shock solution and solitary solution is discussed.
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