Abstract
On the basis of classical linear theory on longitudinal, torsional and flexural waves in thin elastic rods, and taking finite deformation and dispersive effects into consideration, three kinds of nonlinear evolution equations are derived. Qualitative analysis of three kinds of nonlinear equations are presented. It is shown that these equations have homoclinic or heteroclinic orbits on the phase plane, corresponding to solitary wave or shock wave solutions, respectively. Based on the principle of homogeneous balance, these equations are solved with the Jacobi elliptic function expansion method. Results show that existence of solitary wave solution and shock wave solution is possible under certain conditions. These conclusions are consistent with qualitative analysis.
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Communicated by CHENG Chang-jun
Project supported by the National Natural Science Foundation of China (No. 10772129) and the Youth Science Foundation of Shanxi Province of China (No. 2006021005)
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Zhang, Sy., Liu, Zf. Three kinds of nonlinear dispersive waves in elastic rods with finite deformation. Appl. Math. Mech.-Engl. Ed. 29, 909–917 (2008). https://doi.org/10.1007/s10483-008-0709-2
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DOI: https://doi.org/10.1007/s10483-008-0709-2