STICK-SLIP VIBRATIONS OF A 2-DEGREE-OF-FREEDOM GEOPHYSICAL FAULT MODEL

This paper considers the behaviour of a two degree-of-freedom autonomo us system with static and dynamic friction consisting of two blocks li nked by springs on a moving belt. This system is the simplest model wh ich has been used to simulate the dynamics of seismic faults. The fric tion force is assumed to be a decreasing function of the relative slid ing velocity. The motion of the blocks is composed of a uniform stick motion, during which the divergence of the system is zero, and an acce lerated slip motion, during which the divergence is positive. The math ematical 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 Poincare map and a scalar single va riable 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 Lyapu nov exponents, can be easily calculated which provide information rega rding the system-sensitive dependence on initial conditions. The syste m dynamics illustrate the idea of studying the earthquake generation m echanism as a chaotic phenomenon.