SOME EFFECTS OF THRESHOLD SINGULARITIES ON A DYNAMICAL SYSTEM WITH INTERMITTENT CONTACT AND BREAKAGE

A study is presented of the vibration of a mechanical oscillator which is subjected to intermittent contact with a series of elastic-brittle teeth. This mechanical system models in a fundamental way the process of an ice sheet impinging against an elastic structure. The relative displacement of the elastic tooth is an important indicator variable; characteristic values of this indicator establish the breakage of an e lastic tooth and the separation of the oscillator from a tooth, thereb y controlling the dynamics of the system. The Poincare mappings derive d for a particular system of this type are presented. It is found that two types of singularities in the indicator variable functions result in discontinuities and inaccessible subsets in the Poincare sections. These discontinuities provide a basis for establishing limitations of the system's response. The effects of these singularities on a more r ealistic system with random uncertainties is then presented. (C) 1995 Academic Press Limited.