Abstract:Piecewise smooth vibration isolation system is a class of nonlinear dynamics system with piecewise sti ness or damping, which can be found widely in vibration control engineering. This nonlinearity can achieve vibration isolation system's specified dynamics behaviour and improve its e ectiveness, but it will also bring some undesired nonlinear dynamics phenomena, such as amplitude sudden jump, period-doubling bifurcation, etc. The object of this paper is to study the design methodology for piecewise bilinear sti ness vibration system in the view of nonlinear dynamics. First, the entire picture of topology characteristic of frequency response for primary resonance is obtained through combining average method and singularity theory. Results show that the entire parameter plane is divided into four parts and the jump can be induced by both saddle-node and grazing bifurcation. Based on the results, the design principle of amplitude jump avoidance is presented. Then, the Poincaré map for periodic response in e ective isolation band is constructed, and the approach to avoid period-doubling bifurcation is given via eigenvalue analysis. It is verified that the stronger linear damping can suppress the period-doubling bifurcation. Last, this paper studies the e ect of noise on multi-steady state motion for piecewise smooth vibration isolation system. We find that the noise induces that the system's response transfer between the di erent steady states and it is adverse for vibration isolation.