带非线性弹簧的两自由度准零刚度隔振系统力传递率特性

基于多自由度系统中的反共振特性，分别在传统线性隔振系统的上、下两层引入非线性倾斜弹簧负刚度机构，构成两自由度准零刚度隔振器。通过静态特性分析，推导出系统满足零刚度条件时，各参数之间的关系，分析了力学参数及结构参数对系统刚度特性的影响。建立两自由度准零刚度隔振系统的非线性动力学方程，利用平均法求解，推导出力传递率表达式，结合数值分析方法，探讨系统在不同的上、下层隔振器阻尼比、竖直刚度比及质量比情况下的力传递率特性，并与单自由度准零刚度隔振系统及线性斜弹簧两自由度准零刚度隔振系统进行对比研究。结果表明：当结构参数 （即：倾斜弹簧处于静平衡位置的长度与倾斜弹簧原长的比值）较小且倾斜弹簧为软化弹簧时，可在平衡位置附近获得较小的系统刚度及较大的低刚度区间；通过选择适当的上、下层隔振器阻尼比、竖直刚度比与质量比，可减小系统的起始隔振频率，增宽隔振频带，加快系统力传递率在特定频段内的衰减速率，改善系统的低频隔振性能。

Force Transmissibility 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 systems, negative-stiffness structures containing nonlinear inclined springs are introduced into both the upper and lower layers of a traditional linear vibration isolation system to form a two-degree-of-freedom quasi-zero-stiffness vibration isolator. First, through the analysis of static characteristics, a set of relations between the parameters of a quasi-zero-stiffness isolation system is derived. The influences of mechanical and structural parameters on stiffness characteristics of the system are studied. Then, the nonlinear dynamic equations of the two-degree-of-freedom vibration isolation system with quasi-zero stiffness are established. Using the averaging method, the frequency-domain analytical solutions and the expression of force transmissibility are derived. The effects of upper damping ratio, lower damping ratio, vertical stiffness ratio and mass ratio on force transmissibility are numerically discussed. The vibration isolation performance of the two-degree-of-freedom quasi-zero-stiffness vibration isolation system with nonlinear inclined springs is compared with that of the single-degree-of-freedom quasi-zero-stiffness vibration isolation system. The results indicate that the smaller the structural parameter (i.e. the ratio of length when the nonlinear inclined springs are at static equilibrium and initial positions) is, or the softer the nonlinear inclined springs are, the smaller stiffness of the system and the larger low-stiffness interval near the equilibrium position can be obtained. Furthermore, by selecting suitable values of the upper damping ratio, lower damping ratio, vertical stiffness ratio and mass ratio, the initial vibration isolation frequency of the system can be reduced, the vibration isolation band width can be further expanded, the attenuation rate of the force transmissibility in a certain frequency region can be obviously accelerated, and the low-frequency vibration isolation performance of the system can be dramatically improved.