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Stick-slip vibrations of a two degree-of-freedom geophysical fault model. (English) Zbl 0841.70016

The paper considers the complex dynamics of a four-dimensional autonomous stick-slip system which consists of two blocks linked by springs on a moving belt. The friction law is assumed to be a decreasing function of the relative sliding velocity. This system is the simplest model which has been used to simulate the dynamics of seismic faults. 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. 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. The system dynamics illustrates the idea of studying the earthquake generation mechanism as a chaotic phenomenon.

MSC:

70K40 Forced motions for nonlinear problems in mechanics
37B99 Topological dynamics
86A15 Seismology (including tsunami modeling), earthquakes
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