Slowly decaying strain solitons in nonlinear viscoelastic waveguides

TL;DR

This paper models longitudinal strain waves in nonlinear viscoelastic rods using a damped Boussinesq equation, deriving slowly-decaying strain solitons that align well with 3D simulations and highlight the importance of frequency-dependent elastic constants.

Contribution

It introduces a novel damped Boussinesq-type model for strain waves in nonlinear viscoelastic materials with frequency-dependent elastic constants, deriving and validating slowly-decaying soliton solutions.

Findings

Derived a damped Boussinesq equation incorporating frequency-dependent dissipation.

Obtained slowly-decaying strain soliton solutions consistent with 3D simulations.

Highlighted the significance of frequency dependence of elastic constants in strain soliton behavior.

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.