Stochastic Response of Degrading Elastic Systems

Abstract

The dynamic response of mechanical/structural systems and degradation processes due to dynamics has mostly been analysed without the appropriate mutual coupling. In this paper a joint (coupled) description of the system dynamics and the associated degradation process is presented. After general formulation of the problem we consider a randomly vibrating linear elastic system with stiffness degradation due to fatigue. The vibration-degradation problem is represented by the vibration equation with a special (nonlinear) stiffness degradation term. The solution of this equation (the approximate probability density) is obtained by the modified maximum entropy method and the results of associated numerical calculations are illustrated graphically.