Explicit travelling wave solutions in a magneto-electro-elastic circular rod
The abstract A modified (G/G)-expansion method is proposed for constructing exact travelling wave solutions of nonlinear wave equations, and this method finds travelling wave solutions in a straightforward manner and in a neat and helpful form than (G/G)-expansion method. The abundant exact travelling wave solutions of nonlinear longitudinal wave equation(NLWE) with dispersion caused by the transverse Poisson\'s effect in a long magneto-electro-elastic(MEE) circular rod are successfully obtained by the modified (G/G)-expansion method. The relation between solitary wave velocity with wave number are derived strictly. Numerical examples are further presented for the wave in a rod made of five different materials. The obtained results show that the solitary wave not only exists in such rods but also shows different features in different materials, which could have potential applications in non-destructive evaluation of structures made of the advanced MEE material.
Keywords: magneto-electro-elastic(MEE), modified (G¡¯/G)-expansion method, Riccati like equation, travelling wave solution, exact solution.
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ABOUT THE AUTHORS
Xinmou Ma
College of Mechatronic Engineering, North University of China,Taiyuan, 030051, P.R. China
Yutian Pan
College of Mechatronic Engineering, North University of China,Taiyuan, 030051, P.R. China
Liezhen Chang
College of Science, North University of China, Taiyuan, 030051, P.R. China
Xinmou Ma
College of Mechatronic Engineering, North University of China,Taiyuan, 030051, P.R. China
Yutian Pan
College of Mechatronic Engineering, North University of China,Taiyuan, 030051, P.R. China
Liezhen Chang
College of Science, North University of China, Taiyuan, 030051, P.R. China
