Modeling and identification of a vibration isolation system with hysteretic damping

A model to describe the hysteresis damping character of rubber isolation system is presented. It consists of a parallel spring and damper, whose coefficients change with vibration frequencies. In order to acquire these relations, a force decomposition is carried out according to some sine vibration measurement data about nonlinear forces changing with deformations of the rubber material. The nonlinear force is decomposed into a spring force and a damper force, which are represented by a frequency-dependent spring and damper coefficient, respectively. Then, application of a system identification method will provide the requested functions over frequency. Using those formulae, as an example, the dynamic character of a hollow shaft system supported by rubber rings is analyzed and the acceleration response curve in the centroid position is calculated.