Bifurcation characteristics and stability of nonlinear vibration isolation system with fractional differential

Abstract

The vibration isolation components with viscoelastic and nonlinear characteristics of rubber are simulated by establishing a fractional nonlinear Zener model. The fractional differential terms are treated by Caputo definition, and the dynamic performance of the system is simulated by numerical simulation. The periodic motion stability and motion transition law of the system are studied by establishing Poincaré mapping, and the motion stability is determined by combining the maximum Lyapunov exponent. It is found that the fractional differential term defined by Caputo can not only be equivalent to the linear spring stiffness and linear damping coefficient, but also related to the frequency of external excitation. With the decrease of the external excitation frequency, the nonlinear system with fractional differential produces two different attractors under the induction of fork bifurcation, and the number of attractors doubles under the induction of period-doubling bifurcation. after the system enters the chaotic motion, under the induction of cataclysmic bifurcation, different attractors combine with each other as a whole, and the phase trajectory of the system transforms into a single symmetric chaotic motion.