Slow periodic oscillation without radiation damping: New evolution laws for rate and state friction

TL;DR

This paper investigates the possibility of stable periodic oscillations in rate and state friction without radiation damping, proposing two new evolution laws that can produce such oscillations and discussing their relevance to slow earthquakes.

Contribution

It introduces two novel evolution equations for the state variable that enable stable periodic motion without radiation damping, addressing a key gap in existing friction models.

Findings

Existing major evolution laws fail to produce stable periodic motion without radiation damping.

Two new evolution equations are proposed that can generate stable periodic oscillations.

The new laws are evaluated for experimental validity and relevance to slow earthquakes.

Abstract

The dynamics of sliding friction is mainly governed by the frictional force. Previous studies have shown that the laboratory-scale friction is well described by an empirical law stated in terms of the slip velocity and the state variable. The state variable represents the detailed physicochemical state of the sliding interface. Despite some theoretical attempts to derive this friction law, there has been no unique equation for time evolution of the state variable. Major equations known to date have their own merits and drawbacks. To shed light on this problem from a new aspect, here we investigate the feasibility of periodic motion without the help of radiation damping. Assuming a patch on which the slip velocity is perturbed from the rest of the sliding interface, we prove analytically that three major evolution laws fail to reproduce stable periodic motion without radiation damping. Furthermore, we propose two new evolution equations that can produce stable periodic motion without radiation damping. These two equations are scrutinized from the viewpoint of experimental validity and the relevance to slow earthquakes.