The natural frequency is the key performance parameters of a rubber materials damper, and it is determined by the static and dynamic shear properties of the rubber materials (rubber ring) and the moment of inertia of the inertia ring. The rubber ring is usually in compression state, and its static and dynamic shear properties are dependent on its sizes, compression ratio and chemical ingredients. A special fixture is designed and used for measuring static and dynamic shear performance of a rubber ring under different compression ratios in the study. To characterize the shear static and dynamic performances of rubbers, three constructive models (Kelvin-Voigt, the Maxwell and the fractional derivative constitutive model) are presented and the method for obtaining the model parameters in the fractional derivative constructive models are developed using the measured dynamic performance of a rubber shear specimen. The natural frequency of a rubber materials damper is calculated using the fractional derivative to characterize the rubber ring of the damper, and the calculated frequencies are compared with the measurements.

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