Nonlinear dynamic modelling of rubber isolators using six parameters based on parabolic spring, springpot, and smooth-slip friction element

A time-domain six-parameter model is adopted to simulate the vibration behaviour of rubber isolators over the frequency range of 0.05-25 Hz. The one-dimensional model working under constant preload and temperature is capable of producing force as a function of displacement excitation. The model consists of three components, including a nonlinear parabolic spring, a fractional-derivative-based springpot and a smooth-slip friction element. In order to obtain all required six parameters, a novel standard procedure is proposed based on a two-stage optimization method using two sets of data measured in both amplitude and frequency domains. A number of isolators with differences in shape, composition and mode of deformation are selected for study. The consistency of the proposed optimization method and the accuracy of the obtained model are verified by good agreements between measured and simulated results of stiffness and damping across the ranges of investigated displacement amplitudes and frequencies.