STABILITY, BIFURCATION AND CHAOS OF NONLINEAR STRUCTURES WITH CONTROL .2. NONAUTONOMOUS CASE

A single-degree-of-freedom structural model with a non-linear soft spring, a linear damper and a linear displacement feedback control was studied in Part I without the forcing function (autonomous system). In Part II, a harmonic forcing is applied which generates richer mechanical response including chaotic vibrations and fractal basin boundaries. Despite the increased complexity, a perturbation analysis based on Melnikov's function is found applicable to predict the existence of chaotic responses. This analytic prediction, together with the bifurcation conditions obtained in Part I, serves as a guideline in our numerical simulation studying the stability and effectiveness of non-linear structural control.