Nonlinear shear wave interaction at a frictional interface: Energy dissipation and generation of harmonics

TL;DR

This paper investigates how shear waves interact with frictional interfaces, analyzing energy dissipation and harmonic generation through analytical and numerical models, revealing universal laws and potential for friction quantification.

Contribution

It introduces a combined analytical and numerical approach to study nonlinear shear wave interactions at frictional interfaces, highlighting universal behaviors and measurement techniques.

Findings

Higher harmonics amplitude scales with pre-stress and incident amplitude.

Dissipated energy follows universal laws based on non-dimensional parameters.

Harmonic measurements can quantify interface friction and dissipation.

Abstract

Analytical and numerical modelling of the nonlinear interaction of shear wave with a frictional interface is presented. The system studied is composed of two homogeneous and isotropic elastic solids, brought into frictional contact by remote normal compression. A shear wave, either time harmonic or a narrow band pulse, is incident normal to the interface and propagates through the contact. Two friction laws are considered and their influence on interface behavior is investigated : Coulomb's law with a constant friction coefficient and a slip-weakening friction law which involves static and dynamic friction coefficients. The relationship between the nonlinear harmonics and the dissipated energy, and their dependence on the contact dynamics (friction law, sliding and tangential stress) and on the normal contact stress are examined in detail. The analytical and numerical results indicate universal type laws for the amplitude of the higher harmonics and for the dissipated energy, properly non-dimensionalized in terms of the pre-stress, the friction coefficient and the incident amplitude. The results suggest that measurements of higher harmonics can be used to quantify friction and dissipation effects of a sliding interface.