中文摘要：

在Bernoulli-Euler梁，Rayleigh修正梁和Timoshenko梁三种梁理论的基本方程中，分别引入有限挠度和轴向惯性，导出了相应的支配弯曲波传播的非线性偏微分方程组。采用行波解法，并运用某些积分技巧，将每个方程组转化为对应的单个常微分方程。定性分析表明，在一定条件下这些方程在相平面上存在同宿轨道或异宿轨道，分别对应着孤立波解和冲击波解。根据齐次平衡原理，用Jacobi椭圆函数展开对这些常微分方程求解，给出了精确的周期解及其模数m→1退化情况下的孤立波解或冲击波解，与定性分析完全一致。对三种方程解的分析表明，在通常关心的长波条件下，仅有有限挠度Timoshenko梁中的周期波解和冲击波解才有实际意义。

英文摘要：

On the basis of the equation of Bernoulli-Euler, Rayleigh and Timoshenko beam theories, taking finite-deflection and axial inertia into consideration, the nonlinear partial differential equations governing flexural wave propagation were derived. When employing the method of traveling wave solution, the nonlinear partial differential equations were transformed into an ordinary differential equation by using certain integral skills. The qualitative analyses indicate that the three kinds of equations have heteroclinic orbit corresponding shock wave solution or homoclinic orbit corresponding solitary wave solution. On the basis of the principle of homogeneous balance, these equations were resolved by Jacobi elliptic function expansion method and the exact periodic solutions were obtained. With the modulus of Jacobi elliptic functionin m→1 in the degenerate case, the shock wave or solitary wave solution were given. The existence condition of these solutions is c0 〈c. It should be pointed out that for practical purpose only the periodic wave and shock wave solutions in finite-deflection Timoshenko beam are significant.