Nonlinear dynamics and design for a class of piecewise smooth vibration isolation system

Piecewise smooth vibration isolation system is a class of nonlinear dynamics system with piecewise stiffness or damping, which can be found widely in practical engineering. Such nonlinearity can achieve specified dynamics behaviors for vibration isolation system and improve its energy isolation effectiveness, but it will also bring some unexpected nonlinear dynamics phenomena, such as sudden amplitude jump, period-doubling bifurcation. The object of this paper was to study the design methodology for piecewise bilinear stiffness 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, and the design principle of amplitude jump avoidance is obtained. Then, the Poincaré map for periodic response in effective isolation band is constructed, and the approach to avoiding period-doubling bifurcation is also given via eigenvalue analysis. Last, this paper studies the effect of noise on multi-steady state motion for piecewise smooth vibration isolation system and some design suggestions are given.