Force transmissibility of a two-stage vibration isolation system with quasi-zero stiffness

A quasi-zero stiffness (QZS) vibration isolator outperforms other passive control strategies in vibration attenuation especially in a low-frequency band, but it also has an intrinsic limitation of low roll-off rate in the effective frequency range of vibration isolation. To overcome this limitation, a two-stage QZS vibration isolation system (VIS) is proposed, in which the QZS feature is realized by combining a vertical liner spring with two parallel cam-roller-spring mechanisms. Considering a possible disengagement between the cam and the roller under large amplitude vibration, a piecewise nonlinear dynamical model is developed and approximately solved by the averaging method. The analytical solutions for amplitude-frequency relationship and force transmissibility are derived. The results reveal that the two-stage QZS VIS has both advantages of low-frequency vibration isolation and high roll-off rate. It is also found that the second resonance can be eliminated when heavy damping is present in the upper stage, and hence, a broader effective frequency range of isolation can be achieved. High intermediate mass and soft vertical springs in the lower stage are also found to result in high-quality isolation performance.