非线性弹性杆中的应变孤波

以圆杆波导为研究对象,考虑了由应力应变关系导致的物理非线性、横向惯性、横向剪切效应共同作用下的非线性波的传播,利用Hamilton变分原理导出了非线性纵向波动方程。针对非线性波动问题中,对非线性演化方程的定性分析和寻找其精确解存在只能求得非线性波动方程的冲击波解或弧波解,不能求得非线性方程的精解周期解的状况,利用Jacobi椭圆正弦函数展开法,对导出的非线性弹性圆杆波导非线性波动方程进行了求解,得到了该方程的准确周期解以及相对应的孤波解。

Strain Solitary Wave in Nonlinear Elastic Rod

A new nonlinear wave equation in nonlinear circular-rod waveguide taking account of the nonlinear constitutive relationship and transverse inertia and shear effects is derived by means of Hamilton principle.Many methods have been proposed to construct exact solutions to nonlinear equations,however,only shock wave solution or solitary wave solution can be obtained generally and exact periodic solution can't be given from these methods.By using Jacobi elliptic sine function expansion method the nonlinear wave equation is solved,the exact periodic solution of the nonlinear equation is obtained,and may degenerate as the solitary wave solution.