Global Analyses of Multi-Degree-of-Freedom Nonlinear Vibration Isolation System

Abstract

The abundant and complex dynamics of high-dimensional nonlinear systems have drawn increasing attentions in recent years, but further analyses have been confined because of the inefficiency of some analytic methods for high-dimensional systems. This paper focuses on the bifurcation and global analyses of a multi-degree-of-freedom nonlinear vibration isolation system using numerical methods. Firstly, the equations of motion of the multi-degree-of-freedom nonlinear vibration isolation system for onboard machine are formulated. Then, exhaustive bifurcation analyses are carried out and six branches are illustrated in the bifurcation diagrams revealing that several different types of stable motions may coexist in certain parameter regimes. A cell mapping method is modified to analyze the global characteristics including the locations and basins of the coexistent attractors of the multi-degree-of-freedom nonlinear vibration isolation system.