Fractional-order viscoelastic modeling of the magnetic field dependent transmissibility response of MRE isolator

Abstract

In the present study, a modeling approach to estimate the parameters of the MRE isolator model with respect to the frequency-response curve is presented. To concur the response of the isolator over wide frequency range, fractional order based Kelvin Voigt model comprised of three parameters and the fractional Zener model having four parameters are proposed. An isolator operating in shear-mode is developed, and its performance is evaluated through the transmissibility tests. The parameters of the model are identified by minimizing the error between the transmissibility response from the MRE isolator model and the experimental results. A polynomial function is used to generalize the variation of these parameters with respect to the input current. The response predicted by the MRE isolator models confirms that both fractional Kelvin Voigt and fractional Zener modeling approaches are effective in portraying the transmissibility response. The fractional Zener MRE isolator model is more accurate and can reproduce the experimentally determined magnitude and phase response of the transmissibility with an accuracy greater than 91.5% and 84.87% respectively. On the contrary, the fractional Kelvin Voigt model is simpler in form, and it effectively reproduced the magnitude of the transmissibility response with an accuracy higher than 86.35% and the phase response greater than 83.77%.