Integrated design of quasi-zero-stiffness vibration isolators based on bifurcation theory

Isolators with quasi-zero-stiffness (QZS) for isolating undesired vibrations have attracted immense attention from researchers in recent years. They are usually constructed by combining positive and negative stiffness elements in parallel. Such design approach based on two separate elements cannot take full advantage of novel structures such as origami-inspired structures. In this paper, an integrated design approach for QZS isolators is proposed based on bifurcation theory. The effects of preload of the isolators can also be introduced. A theoretical method for achieving QZS property is proposed by finding the design parameters corresponding to the supercritical pitchfork bifurcation. Another case inspired by supercritical pitchfork bifurcation is also proposed (i.e., named CISP) for realizing QZS property. Based on the proposed approach, a QZS isolator under preload is designed with stacked Miura-origami units. The design process, including the geometric analysis of the units and achievement of QZS property, is first elaborated. The dynamic model of the isolator is established and validated by rigid body dynamics simulation, followed by the vibration isolation performance evaluation. The results show that the designed origami-based vibration isolator can achieve ultra-low frequency of isolation and peak transmissibility under excitation with small amplitude and/or high damping. The proposed design method paves the way to develop high-efficiency vibration isolators with QZS property for vibration engineering applications.