Periodic-Doubling and Hopf Bifurcations of a Two-Degree-of-Freedom System with Elastic Constraints and Clearances

Based on the study of a dual component system with elastic constraints, the stability and local bifurcations of the soft-impacts system, such as piecewise property and singularity, was analyzed by using the Poincare map and Runge-Kutta numerical simulation method. The routes from periodic motions to chaos, via Hopf bifurcation and period-doubling bifurcation, were investigated exactly. In the large constraint stiffness case, the period-doubling and Hopf bifurcation exist in the two-degree-of-freedom system with elastic constraints and clearances. The clearances of the system, stiffness and damping coefficient of the elastic constraints is the main reasons for influencing the chaotic motion. The steady 1-1-1 period orbits or 2-1-1 period orbits will exist within a wideband frequency range and the value of velocity will be higher when appropriate system parameters are chosen.