Slowly decaying strain solitons in nonlinear viscoelastic waveguides
Abstract
This paper is devoted to the modeling of longitudinal strain waves in a rod composed of a nonlinear viscoelastic material characterized by frequency-dependent second- and third-order elastic constants. We demonstrate that long waves in such a material can be effectively described by a damped Boussinesq-type equation for the longitudinal strain, incorporating dissipation through retarded operators. Using the existing theory of solitary wave solutions in nearly integrable systems, we derive a slowly-decaying strain soliton solution to this equation. The derived soliton characteristics are shown to be in a good agreement with results from full 3D simulations. We demonstrate the importance of taking into account the frequency dependence of third-order elastic constants for the description of strain solitons.
Cite
@article{arxiv.2501.09415,
title = {Slowly decaying strain solitons in nonlinear viscoelastic waveguides},
author = {F. E. Garbuzov and Y. M. Beltukov},
journal= {arXiv preprint arXiv:2501.09415},
year = {2025}
}