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Solitary waves and chaos in nonlinear visco-elastic rod

✍ Scribed by Nianmei Zhang; Guitong Yang

Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
232 KB
Volume
22
Category
Article
ISSN
0997-7538

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✦ Synopsis

The dynamics behavior of a nonlinear visco-elastic rod subjected to axially periodic load is investigated theoretically and numerically. The weak longitudinal periodic load is distributed uniformly along the rod. Firstly, equation of motion of the rod is derived. Utilizing perturbation technique, we acquire Kdv type equation describing strain wave in the rod. By use traveling wave method, the elliptic cosine wave solution and the solitary wave solution in the rod are provided. Then, Melnikov method is applied to analyze the dynamic behaviour of the rod qualitatively. The explicit conditions for the onset of chaotic dynamics are yielded. With the help of the Poincare map method, phase trajectory and time-displacement history diagrams, the theoretical results obtained are checked.

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