Characterization and dynamical stability of fully nonlinear strain solitary waves in a fluid-filled hyperelastic membrane tube

Fu

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.

Citation

Fu. (2020). Characterization and dynamical stability of fully nonlinear strain solitary waves in a fluid-filled hyperelastic membrane tube. Acta mechanica, https://doi.org/10.1007/s00707-020-02754-z

• Acceptance Date: May 26, 2020
• Publication Date: Jul 8, 2020
• Journal: Acta Mechanica
• Print ISSN: 0001-5970
• Publisher: Springer Verlag
• DOI: https://doi.org/10.1007/s00707-020-02754-z
• Publisher URL: https://link.springer.com/article/10.1007%2Fs00707-020-02754-z