The response of stick-slip systems to random seismic excitation

Abstract

This thesis examines the response of stick-slip, or frictional, systems to harmonic and random excitation. Two frictional models are considered: constant slip force, or Coulomb, friction, and displacement dependent slip force, used to model a caster, or pivoting wheel. The response to harmonic excitation of systems exhibiting both frictional models is determined using the method of slowly varying parameters. Changes in the response amplitude of both systems caused by the addition of a linear centering mechanism are also examined. The response of the system with displacement dependent slip force is examined under Gaussian mean zero white noise excitation using the generalized equivalent linearization method. It is shown that a lower bound is obtained from the Coulomb friction system's response. For filtered random excitation, linearization methods are shown to predict erroneous displacement trends for the Coulomb system when the input has no spectral content at zero frequency. When the excitation is modeled as a Poisson pulse process, an approximate method exhibiting the proper displacement trends can be constructed. The method is shown to be accurate over a broad range of input parameters if overlaps in the input pulses are considered. A set of excitation parameters consistent with seismic events is then used to estimate final rms displacements as a function of coefficient of friction.