Shock Waves and Solitary Waves in Elastic Circular Rod

Abstract:

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.

• Periodical: Advanced Materials Research (Volumes 183-185)
• Pages: 2197-2201
• DOI: https://doi.org/10.4028/www.scientific.net/AMR.183-185.2197
• Online since: January 2011
• Authors: Zhi Fang Liu, Yuan Yuan He, Shan Yuan Zhang
• Keywords: Finite Deformation, Hyperbolic Cotangent Function, Hyperbolic Tangent Function, Nonlinear Wave, Poisson Effect

References

[1] Whitham G.B., Linear and Nonlinear Waves, (John Wiley &Sons, New York 1974).

[2] Yang Guitong, Zhang Shanyuan, Dynamic Elasticity, (Chinese Railway Press 1988, Beijing).

[3] Zhang Shanyuan, Zhuang wei, Acta mechanica sinia Vol. 1(1987) p.62.

[4] Alexei V. Porubov, Manuel G. Velarde, C.R. Acad. Sci. Series II b (2000), p.165.

[5] Wang Mingliang, Physics Letter A Vol. 199 (1995). P. 169.

[6] Yan Chuntao, Physics Letter A Vol. 224 (1996). p.77.

[7] Zheng Xuedong, Xia Tiecheng, Zhang Hongqing, Applied Mathematics E-Notes Vol. 2(2002), p.42.

[8] Liu Shikuo, Fu Zun tao, Liu Shida etc., Applied Mathematics and Mechanics Vol. 22 (2001), p.326.

[9] Zhang Jiefang, International Journal of Theoretical Physics Vol. 37 (1998), p.1541.

[10] Liu Zhifang, Zhang Shanyuan, Acta Mechanica Solida Sinica Vol. 19(2006), p.1.