Study on Strain Solitary Waves in the Nonlinear Elastic Circular Rod

Abstract:

Taking into account the nonlinear constitutive relationship and transverse Poisson effects, the propagation characteristic of nonlinear wave for one-dimension elastic thin rod is studied. With the help of Mathematic, two traveling wave solutions for this nonlinear wave equation are obtained by sine-cosine function method, which include the shock wave solution and the solitary wave solution. The necessary condition of these solutions is given also.

• Periodical: Advanced Materials Research (Volumes 97-101)
• Pages: 691-694
• DOI: https://doi.org/10.4028/www.scientific.net/AMR.97-101.691
• Online since: March 2010
• Authors: Zhi Fang Liu, Shan Yuan Zhang, Guo Yun Lu
• Keywords: Nonlinear Wave, Sine-Cosine Method, Transverse Poisson Effect

References

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

[2] P.L. Bhatnager: �onlinear Waves in One-dimensional Dispersive System (Clarendon Press, Oxford 1979).

[3] W.Q. Zhu: Acta Mech. Solida Sin. Vol. 2 (1980), p.247 (In Chinese).

[4] S.Y. Zhang and W. Zhuang: Acta Mech. Sin. Vol. 1 (1987), p.62.

[5] Z.F. Liu and S.Y. Zhang: Acta Phys. Sin. Vol. 54 (2006)，p.628 (In Chinese).

[6] M.J. Abeowitz, P.A. Clarkson: �onlinear evolution Equation and Inverse Scatting (Cambridge University Press, New York 1991).

[7] Z.Y. Yan, H.Q. Zhang and E.G. Fan: Acta Phys. Sin. Vol. 48 (1999), p.1 (In Chinese).

[8] X.D. Zheng, T.C. Xia and H.Q. Zhang: Appl. Math. E-Notes Vol. 2 (2002), p.45.

[9] J.F. Zhang: Int. J. Theor. Phys. Vol. 37 (1998), p.1541.