Shock Waves and Solitary Waves in Elastic Circular Rod
A nonlinear waves equation of an elastic circular rod taking account of finite deformation and transverse Poisson effect is derived by means of Hamilton variation principle in this paper. Nonlinear wave equation and corresponding truncated nonlinear wave equation are solved by the hyperbolic tangent function and cotangent function finite expansion method. Two different types of exact traveling wave solutions, the shock wave solution and the solitary wave solution are obtained. The necessary condition of these solutions existence is given also.
Yanguo Shi and Jinlong Zuo
Z. F. Liu et al., "Shock Waves and Solitary Waves in Elastic Circular Rod", Advanced Materials Research, Vols. 183-185, pp. 2197-2201, 2011