Relaxation damping in oscillating contacts

TL;DR

This paper introduces and analytically characterizes relaxation damping, a unique energy dissipation effect in elastic contacts under oscillations, independent of friction or material dissipation, with potential applications as a tunable damper.

Contribution

It provides a closed-form analytical description of relaxation damping in elastic contacts, including its dependence on oscillation parameters and phase shift, and discusses generalization to rough surfaces.

Findings

Energy dissipation is proportional to the square of tangential amplitude.

Dissipated energy depends on phase shift between oscillations.

The system can function as a tunable linear damper.

Abstract

If a contact of two purely elastic bodies with no sliding (infinite coefficient of friction) is subjected to superimposed oscillations in the normal and tangential directions, then a specific damping appears, that is not dependent on friction or dissipation in the material. We call this effect "relaxation damping". The rate of energy dissipation due to relaxation damping is calculated in a closed analytic form for arbitrary axially-symmetric contacts. In the case of equal frequency of normal and tangential oscillations, the dissipated energy per cycle is proportional to the square of the amplitude of tangential oscillation and to the absolute value of the amplitude of normal oscillation, and is dependent on the phase shift between both oscillations. In the case of low frequency tangential motion with superimposed high frequency normal oscillations, the system acts as a tunable linear damper. Generalization of the results for macroscopically planar, randomly rough surfaces is discussed.