| Abstract: | This paper considers the behaviour of a two degree-of-freedom autonomous system with static and dynamic friction consisting of two blocks linked by springs on a moving belt. This system is the simplest model which has been used to simulate the dynamics of seismic faults. The friction force is assumed to be a decreasing function of the relative sliding velocity. The motion of the blocks is composed of a uniform stick motion, during which the divergence of the system is zero, and an accelerated slip motion, during which the divergence is positive. The mathematical model by definition concentrates the dissipation on the point where the slip motion ceases. It is assumed that slip occurs only in one direction. A three-dimensional Poincaré map and a scalar single variable map are discussed which characterize the dynamics of the system in a simple way. The one-dimensional map can be used to diagnose the chaotic behaviour of the full system, and quantities, similar to Lyapunov exponents, can be easily calculated which provide information regarding the system-sensitive dependence on initial conditions. The system dynamics illustrate the idea of studying the earthquake generation mechanism as a chaotic phenomenon. |
