Nonlinear traveling waves in a compressible Mooney-Rivlin rod I. Long finite-amplitude waves |
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Authors: | Dai Huihui Liu Zengrong |
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Institution: | (1) Department of Mathematics, City University of Hong Kong, Kowloon, Hong Kong, China;(2) Department of Mathematics, Shanghai University, 201800 Shanghai, China |
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Abstract: | In literature, nonlinear traveling waves in elastic circular rods have only been studied based on single partial differential
equation (pde) models, and here we consider such a problem by using a more accurate coupled-pde model. We derive the Hamiltonian
from the model equations for the long finite-amplitude wave approximation, analyze how the number of singular points of the
system changes with the parameters, and study the features of these singular points qualitatively. Various physically acceptable
nonlinear traveling waves are also discussed, and corresponding examples are given. In particular, we find that certain waves,
which cannot be counted by the single-equation model, can arise.
The project supported by the Research Grants Council of the HKSAR, China (City U 1107/99P) and the National Natural Science
Foundation of China (10372054 and 10171061) |
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Keywords: | hyperelastic rod nonlinear traveling waves solitary waves periodic waves |
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