Non-linear behavior of a rubber isolator system using fractional derivatives

A non-linear rubber isolator included in a dynamic system is examined where influences of dynamic amplitude and frequency are investigated through measurements and modeling. The frequency dependence of the isolator is modeled by a fractional calculus element while a frictional component accounts for its amplitude dependence. The model works in the time-domain and simulations of harmonic and non-harmonic motion are compared to measurements. Good agreement is obtained in a wide frequency and amplitude range for a freely oscillating one degree of freedom system, with the isolator acting as a coupling between exciting foundation and mass, and for a single isolator showing the typical amplitude dependence known as the Payne effect. The model is found to be superior to the commonly applied Kelvin-Voigt element in modeling the dynamic isolator properties.