Discontinuous Bifurcations under 2-DOF Vibroimpact System Moving

Abstract

Dynamic behaviour of strongly nonlinear non-smooth discontinuous vibroimpact system isstudied. Under variation of system parameters we find the disconti nuousbi furcati onsthat are the dangerousones. It is phenomenon unique to non-smooth systems with discontinuous right-hand side. We investigate the 2-DOF vibroimpact system by numerical parameter continuation method in conjunction with shooting and Newton-Raphson methods, Wife simulate the impact by nonlinear contact interactive force according to Hertz's contact law. We find the discontinuous bifurcations by Floquet multipliers values. At such points set-valued Floquet multipliers cross the unit circle by jump that istheir moduli becoming more than unit by jump. Wealso learn the bifurcation picture change when the impact between system bodi es became the soft one due the change of system parameters, This paper is the continuation of the previous works.