A new vibro-impact bistable oscillator with an adjustable rigid wall

Abstract

In this paper, a new vibro-impact bistable oscillator under vicious damping and external harmonic excitation is proposed by adding an adjustable rigid wall to one side of the archetypal smooth and discontinuous (SD) oscillator and an impact mapping is given to describe energy loss during collisions. In the unperturbed ideal case, there exist rich and perfect geometrical structure including grazing phenomena such as periodic orbits and homoclinic orbits tangent to the wall due to its adjustability as a constraint. Perturbed dynamics is studied to show the influence of the constraint on the original SD oscillator through the Lyapunov exponent diagrams, bifurcation diagrams, and the corresponding phase diagrams and attractors. Some new non-smooth chaotic attractors and periodic orbits are found to have grazing or transversal interaction with the unilateral rigid wall. Due to the effect of the introduced impact mapping and different locations of the rigid wall, the finger-like chaotic attractors of the SD oscillator will be suppressed and changed into different non-smooth periodic motions by varying the non-dimensional parameter which reflects the degree of the springs compressed, while the periodic motions of the SD oscillator will become new non-smooth chaotic attractors or different non-smooth periodic motions.