Solitary Wave Evolution and Non-Smooth Solitary Waves in Microstructured Solids

NARANMANDULA; HAN Yuanchun; ZHANG Fang

doi:10.21656/1000-0887.390069

Volume 40 Issue 4

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NARANMANDULA, HAN Yuanchun, ZHANG Fang. Solitary Wave Evolution and Non-Smooth Solitary Waves in Microstructured Solids[J]. Applied Mathematics and Mechanics, 2019, 40(4): 433-442. doi: 10.21656/1000-0887.390069

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Solitary Wave Evolution and Non-Smooth Solitary Waves in Microstructured Solids

doi: 10.21656/1000-0887.390069

¹College of Physics and Electronic Information, Inner Mongolia University for Nationalities, Tongliao, Inner Mongolia 028000, P.R.China; ²College of Mathematics, Inner Mongolia University for Nationalities, Tongliao, Inner Mongolia 028000, P.R.China

Funds: The National Natural Science Foundation of China(11462019)

Received Date: 2018-02-05
Rev Recd Date: 2018-12-12
Publish Date: 2019-04-01

Abstract

Abstract

A new free energy function was given with all quadratic terms of macro strain and micro deformation, as well as cubic terms of macro strain. A new model for description of the longitudinal wave propagation in microstructured solids was established by means of the new free energy function and Mindlin’s microstructure theory. Based on the dynamical system theory for singular traveling wave systems developed recently, all bifurcations of phase portraits of the traveling wave systems were analyzed, and the periodic wave solutions, the solitary wave solutions, the quasi peakon solutions, the peakon solutions and the compacton solutions were given. The obtained peakon and compacton solutions effectively prove that non-smooth solitary waves such as the peakon and the compacton can form and exist in microstructured solids under certain conditions. The results further exceed the conclusion that only smooth solitary waves can exist in microstructured solids.
- model,
- microstructured solid,
- non-smooth solitary wave,
- evolution

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References(16)

References

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