Kink and kink-like waves in pre-stretched Mooney-Rivlin viscoelastic rods
The present paper theoretically investigates kink and kink-like waves propagating in pre-stretched Mooney-Rivlin viscoelastic rods. In the constitutive modeling, the Cauchy stress tensor is assumed to consist of an elastic part and a dissipative part. The asymptotic method is adopted to simplify the...
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2015-08-01
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Online Access: | http://dx.doi.org/10.1063/1.4929721 |
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doaj-097ba646b9b94fc195dae964b02b98712020-11-25T00:09:34ZengAIP Publishing LLCAIP Advances2158-32262015-08-0158087167087167-1710.1063/1.4929721066508ADVKink and kink-like waves in pre-stretched Mooney-Rivlin viscoelastic rodsY. Z. Wang0H.-H. Dai1W. Q. Chen2Department of Engineering Mechanics, Zhejiang University, Hangzhou 310027, ChinaDepartment of Mathematics, City University of Hong Kong, Kowloon, Hong Kong, ChinaDepartment of Engineering Mechanics, Zhejiang University, Hangzhou 310027, ChinaThe present paper theoretically investigates kink and kink-like waves propagating in pre-stretched Mooney-Rivlin viscoelastic rods. In the constitutive modeling, the Cauchy stress tensor is assumed to consist of an elastic part and a dissipative part. The asymptotic method is adopted to simplify the nonlinear dynamic equations in the limit of finite-small amplitude and long wavelength. Using the reductive perturbation method, we further derive the well-known far-field equation (i.e. the KdV-Burgers equation), to which two kinds of explicit traveling wave solutions are presented. Examples are given to show the influences of pre-stretch and viscosity on the wave shape and wave velocity. It is shown that pre-stretch could be an effective method for modulating the two types of waves. In addition, such waves may be utilized to measure the viscosity coefficient of the material. The competition between the effects of pre-stretch and viscosity on the kink and kink-like waves is also revealed.http://dx.doi.org/10.1063/1.4929721 |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Y. Z. Wang H.-H. Dai W. Q. Chen |
spellingShingle |
Y. Z. Wang H.-H. Dai W. Q. Chen Kink and kink-like waves in pre-stretched Mooney-Rivlin viscoelastic rods AIP Advances |
author_facet |
Y. Z. Wang H.-H. Dai W. Q. Chen |
author_sort |
Y. Z. Wang |
title |
Kink and kink-like waves in pre-stretched Mooney-Rivlin viscoelastic rods |
title_short |
Kink and kink-like waves in pre-stretched Mooney-Rivlin viscoelastic rods |
title_full |
Kink and kink-like waves in pre-stretched Mooney-Rivlin viscoelastic rods |
title_fullStr |
Kink and kink-like waves in pre-stretched Mooney-Rivlin viscoelastic rods |
title_full_unstemmed |
Kink and kink-like waves in pre-stretched Mooney-Rivlin viscoelastic rods |
title_sort |
kink and kink-like waves in pre-stretched mooney-rivlin viscoelastic rods |
publisher |
AIP Publishing LLC |
series |
AIP Advances |
issn |
2158-3226 |
publishDate |
2015-08-01 |
description |
The present paper theoretically investigates kink and kink-like waves propagating in pre-stretched Mooney-Rivlin viscoelastic rods. In the constitutive modeling, the Cauchy stress tensor is assumed to consist of an elastic part and a dissipative part. The asymptotic method is adopted to simplify the nonlinear dynamic equations in the limit of finite-small amplitude and long wavelength. Using the reductive perturbation method, we further derive the well-known far-field equation (i.e. the KdV-Burgers equation), to which two kinds of explicit traveling wave solutions are presented. Examples are given to show the influences of pre-stretch and viscosity on the wave shape and wave velocity. It is shown that pre-stretch could be an effective method for modulating the two types of waves. In addition, such waves may be utilized to measure the viscosity coefficient of the material. The competition between the effects of pre-stretch and viscosity on the kink and kink-like waves is also revealed. |
url |
http://dx.doi.org/10.1063/1.4929721 |
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