Dynamic characteristics of two degree-of-freedom quasi-zero stiffness vibration isolation system with nonlinear springs

Based on the anti-resonance characteristics of multi-degree-of-freedom system, negative stiffness structures containing nonlinear inclined springs (NIS) are introduced to form a two degree-of-freedom (DOF) quasi-zero stiffness (QZS) vibration isolator. The remarkable feature of this system is the use of nonlinear springs to achieve the nonlinear stiffness. The restoring force generated by the NIS includes both linear stiffness term and cubic stiffness term. First, through static characteristic analysis, the relation between parameters is derived when the system meets QZS conditions. Influences of mechanical and structural parameters on stiffness characteristics are studied. Then, nonlinear dynamic equations of the two DOF vibration isolation system with QZS are established. Using the harmonic balance method, the frequency-domain analytical solutions and expression of force transmissibility are deduced. Effects of damping ratio, vertical stiffness ratio, mass ratio and excitation amplitude on the dynamic response and force transmissibility are numerically discussed. The isolation performance of the system is in comparison with single DOF QZS system and two DOF QZS system with linear inclined springs (LIS). The results indicate that smaller structural parameterE and nonlinear inclined springs with softening stiffness are conducive to obtain smaller system stiffness and larger low-stiffness interval near equilibrium position. Furthermore, by selecting suitable parameters, the system has advantages of achieving the lower initial isolation frequency and wider isolation frequency band. In addition, the attenuation rate of force transmissibility in a certain frequency region is able to be obviously accelerated and the low-frequency isolation performance of the system can be dramatically improved.