IJPAM: Volume 85, No. 6 (2013)

MODULATION WAVE EQUATION FOR SPRING-BLOCK
ORBITS WITH NONLINEAR RATE AND STATE FRICTION

Kodwo Annan
Department of Mathematics & Computer Science
Minot State University
Minot, North Dakota, 58707, USA


Abstract. A four-dimensional parameter model that captures the essence of spring-block propagation with rate- and state- friction laws was stated. In order to establish the existence of waves phenomena for all velocity-dependent critical value of stiffness and stick-slip amplitude for stiffness variations, we derived the modulation equation for our model. Conditions under which the amplitude of the modulation wave equation produces many small solutions near the instability threshold for finitely large enough time scales were established.

Received: April 13, 2013

AMS Subject Classification:

Key Words and Phrases: spring-block, modulation, rate-state-friction, instability threshold, existence

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DOI: 10.12732/ijpam.v85i6.7 How to cite this paper?
Source:
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2013
Volume: 85
Issue: 6