A nonlinear stiffness and nonlinear inertial vibration isolator is proposed in this article. It consists of an inerter, a damper, and spring elements. The nonlinear stiffness characteristic is achieved through a negative stiffness structure based on the diamond-shaped structure that generates nonlinear displacement terms. The nonlinear inertial characteristic is implemented via a geometrical nonlinear inerter that produces a nonlinear acceleration term and a nonlinear quadratic velocity term. An averaging method is developed to analyze approximately the dynamic response. The isolation performance is evaluated using four performance criteria: dynamic displacement peak, force transmissibility peak, isolation frequency band, and high-frequency force transmissibility. The effects of the nonlinear inertial characteristic on the dynamic response and isolation performance are examined. The results show that the backbone curve of the nonlinear stiffness and nonlinear inertial vibration isolator has two changing trends: bending first to the right and then to the left and bending directly to the left. The corresponding frequency response curve displays linear, hardening, and softening characteristics. The isolation performance of the nonlinear stiffness and nonlinear inertial vibration isolator is compared with that of the nonlinear stiffness and nonlinear stiffness and linear inertial ones. It could achieve a smaller force transmissibility peak, lower resonant frequency, and larger isolation frequency band than the nonlinear stiffness one and could have smaller dynamic displacement peak and smaller high-frequency force transmissibility than the nonlinear stiffness and linear inertial one. The proposed nonlinear stiffness and nonlinear inertial vibration isolator achieves a better integrated isolation performance among the three vibration isolators.

本文提出了一种非线性刚度和非线性惯性隔振器。它由一个惰轮，一个阻尼器和多个弹簧元件组成。非线性刚度特性是通过基于产生非线性位移项的菱形结构的负刚度结构实现的。非线性惯性特性是通过产生非线性加速度项和非线性二次速度项的几何非线性惯性来实现的。开发了一种平均方法来近似分析动态响应。隔离性能使用四个性能标准进行评估：动态位移峰值，力传递峰值，隔离频带和高频力传递性。研究了非线性惯性特性对动态响应和隔离性能的影响。结果表明，非线性刚度和非线性惯性隔振器的主干曲线有两个变化趋势：先向右弯曲再向左弯曲，再向左弯曲。相应的频率响应曲线显示线性，硬化和软化特性。比较了非线性刚度和非线性惯性隔振器与非线性刚度，非线性刚度和线性惯性隔振器的隔振性能。可以实现较小的力传递峰，较低的共振频率，隔离频带比非线性刚度一个更大，并且具有比非线性刚度和线性惯性一个小的动态位移峰值和一个较小的高频力传递率。所提出的非线性刚度和非线性惯性隔振器在三个隔振器之间实现了更好的集成隔振性能。