A nonlinear stiffness and nonlinear inertial vibration isolator

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.