Vibration power flow and force transmission behaviour of a nonlinear isolator mounted on a nonlinear base

The vibrational power flow and force transmission characteristics of a two-degree-of-freedom (TDOF) nonlinear system are investigated to examine the performance of a nonlinear isolator. The system consists of a harmonically-excited mass, mounted on a single-degree-of-freedom (SDOF) nonlinear flexible base structure through a nonlinear isolator. Both the isolator and the base exhibit damping and stiffness nonlinearities characterized by cubic damping and cubic restoring forces, respectively. The steady-state response of the system is obtained by using the method of averaging and numerical integrations. The bisection method is developed to solve coupled nonlinear frequency response equations. The time-averaged input, dissipated and transmitted powers of the system in the steady-state motion are formulated. Power transmission ratio is proposed as an isolation performance index and compared with force transmissibility. It is found that softening stiffness nonlinearity in the isolator can reduce power transmission ratio, and suppress the peak values of time-averaged power flow and force transmissibility. In comparison, the hardening stiffness in the isolator can lead to a larger power transmission ratio and larger force transmissibility in the high-frequency range. It is shown that power transmission ratio can be reduced by the damping nonlinearity in the isolator, but is enlarged by that in the base. It is also shown that softening nonlinear isolator may provide a better performance than a hardening isolator when the base is of either hardening or softening stiffness nonlinearity. The paper provides a better understanding of the effects of nonlinearities on the performance of nonlinear vibration isolators and demonstrates their potential application to enhance vibration mitigation.