Chaotic and stochastic dynamics for a nonlinear structural system with hysteresis and degradation

In this paper we attempt to introduce some new and fascinating discoveries in chaotic dynamics with particular emphasis on their relationship with stochastic dynamics. Our investigation centers around the deterministic structural system. We begin with a nonlinear hard or soft spring system governed by the well known Duffing's equation. We then add the important engineering material behaviour of hysteresis and degradation. Under a set of unique initial conditions and a harmonic steady-state excitation, the response for a certain deterministic structural system is found to be stochastic.