Uncertainty modeling for metal-rubber isolator system and its propagation effects on nonlinear vibration responses

This paper proposed an uncertainty quantification strategy from the hysteresis characteristics of the metal-rubber isolator (MRI) element to the nonlinear vibration responses of the MRI system. An innovative phenomenological model was developed to accurately reproduce the hysteresis behavior of the MRI element, and the uncertain model parameters along with their interval distributions were determined through repeated periodic excitation tests. By combining the Chebyshev interval method (CIM) with the Cut-high dimensional model representation (Cut-HDMR), a high-efficiency uncertainty propagation analysis method, CIM-HDMR, was proposed to estimate the vibration response bounds of the MRI system under multidimensional interval uncertainties. The nonlinear vibration responses were obtained through the combination of the harmonic balance method and an alternate frequency/time procedure (AFT-HBM). Additionally, the determined interval parameters were used to construct a clustered parameter space based on sensitivity analysis, which further reduced the effects of overestimation and nonlinearities in traditional interval algorithms. Numerical results revealed a significant effect of uncertain hysteresis behavior on the vibration responses of the MRI system, manifesting as “resonance bands” and “frequency shifts.” The proposed strategy accurately quantified the interval distribution characteristics of vibration responses within the parameter space and elucidated the influence mechanisms of uncertain hysteresis behavior on the MRI system.