Solitary Waves in Finite Deformation Elastic Circular Rod
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摘要: 在同时引入横向惯性和横向剪切应变的情况下，导出了有限变形弹性圆杆的非线性纵向波动方程，方程中包含了二次和三次的非线性项以及由横向剪切与横向惯性导致的两种几何弥散效应．借助Mathematica软件，利用双曲正割函数的有限展开法，对该方程和对应的截断的非线性方程进行求解，得到了非线性波动方程的孤波解，同时给出了这些解存在的必要条件．Abstract: A new nonlinear wave equation of a finite deformation elastic circular rod simultaneously introducing transverse inertia and shearing strain was derived by means of Hamilton principle. The nonlinear equation includes two nonlinear terms caused by finite deformation and double geometric dispersion effects caused by transverse inertia and transverse shearing strain. Nonlinear wave equation and corresponding truncated nonlinear wave equation were solved by the hyperbolic secant function finite expansion method. The solitary wave solutions of these nonlinear equations are obtained. The necessary condition of these solutions existence is given also.
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