Il’íchev, AT, Shargatov, VA and Fu, Y ORCID: https://orcid.org/0000-0002-9617-0420 (2020) Characterization and dynamical stability of fully nonlinear strain solitary waves in a fluid-filled hyperelastic membrane tube. Acta Mechanica.

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Abstract

We first characterize strain solitary waves propagating in a fluid-filled membrane tube when the fluid is stationary prior to wave propagation and the tube is also subjected to a finite stretch. We consider the parameter regime where all traveling waves admitted by the linearized governing equations have nonzero speed. Solitary waves are viewed as waves of finite amplitude that bifurcate from the quiescent state of the system with the wave speed playing the role of the bifurcation parameter. Evolution of the bifurcation diagram with respect to the pre-stretch is clarified. We then study the stability of solitary waves for a representative case that is likely of most interest in applications, the case in which solitary waves exist with speed c lying in the interval $$[0, c_1)$$[0,c1)where $$c_1$$c1is the bifurcation value of c, and the wave amplitude is a decreasing function of speed. It is shown that there exists an intermediate value $$c_0$$c0in the above interval such that solitary waves are spectrally stable if their speed is greater than $$c_0$$c0and unstable otherwise.

Item Type: Article
Additional Information: Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
Subjects: Q Science > Q Science (General)
T Technology > T Technology (General)
T Technology > TA Engineering (General). Civil engineering (General)
Divisions: Faculty of Natural Sciences > School of Computing and Mathematics
Related URLs:
Depositing User: Symplectic
Date Deposited: 30 Jul 2020 12:20
Last Modified: 30 Jul 2020 12:20
URI: https://eprints.keele.ac.uk/id/eprint/8453

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