Single-stage and multi-stage consecutive constant quasi-zero stiffness for vibration isolation at low frequency

Quasi-zero stiffness (QZS) isolators have high static and low dynamic stiffness and widely been focused in the field of the vibration isolation at low frequency. Isolators with nonlinear QZS can’t be used for vibration isolation under variable mass loads because the increased dynamic stiffness caused by mismatched mass load decreases initial frequency of vibration isolation and increases the transmissibility. In order to solve this problem and improve the performance of vibration isolation, an isolator has been designed using tension springs and oblique bars. QZS conditions have been derived, according to which constant QZS, constant zero stiffness or constant force, and nonlinear QZS can be realized as any values desired. The multi-stage consecutive constant QZS is furtherly proposed using the constant QZS. The displacement transmissibility has been derived and calculated by employing the harmonic balance method and the incremental harmonic balance method, and shows the same result with each other. Two prototypes have been fabricated to experimentally study the two vibration isolation mechanisms of variable mass loads. The first mechanism is the single-stage constant QZS to successfully isolate vibrations with small magnitude of variable mass loads, such as 10％ variation of the designed mass load. The second mechanism is the multi-stage consecutive constant QZS, which can be applied to variable mass loads with large magnitude, such as the mass load is 32％ variation of the designed value or larger extent. The two mechanisms of the