An investigation of the dynamic performance of lateral inerter-based vibration isolator with geometrical nonlinearity

Inerter, which is defined as a two-terminal mechanical element, has the characteristic that the force generated at its two terminals is proportional to the relative acceleration of the two ends. In this paper, a vibration isolator with lateral inerters is proposed and the effect of this geometrical nonlinear inerter on its dynamic performance is investigated. The force of the inerters in the moving direction of the mass and the acceleration term in the dynamic equation are nonlinear. The dynamic response is obtained using the averaging method and further checked by the numerical results, the stability analysis is also considered. The critical surface of the structural parameters which leads to no jump phenomenon and the jump frequencies when jump phenomenon occurs are determined by the Sylvester resultant method. The isolation performance of the lateral inerter-based vibration isolator is evaluated using four performance indexes: maximum dynamic displacement, maximum transmissibility, isolation frequency band and transmissibility in the higher isolation frequency band, and is compared with the parallel and series-connected inerter-based vibration isolators, as well as the linear vibration isolator. The results show that when the force amplitude is small, compared with the linear vibration isolator, the lateral inerter-based vibration isolator proposed in this paper can have a smaller maximum force transmissibility and larger isolation frequency band; the force transmissibility in the higher isolation frequency band is the same, which has the corresponding advantages of the parallel and series-connected inerter-based vibration isolators, respectively.