Analytically optimal parameters of fractional-order dynamic vibration absorber

Abstract

In this paper the optimal parameters of the fractional-order Voigt type dynamic vibration absorber (DVA) are analytically studied for two cases, named as H∞ and H2 optimization criteria. At first the approximately analytical solution is obtained by the averaging method when the primary system is subjected to harmonic excitation. Then the optimal fractional coefficient and order are obtained based on H∞ optimization criterion, which is designed to minimize the maximum amplitude magnification factor of the primary system. Based on H2 optimization criterion, the optimal fractional parameters are obtained to reduce the total vibration energy of the primary system over the whole-frequency range. The comparisons of the approximate solutions with the numerical ones in the two cases are fulfilled, and the results verify that the approximately analytical solutions are correct and satisfactorily precise. At last the control performance of the fractional-order Voigt type DVA is compared with the classical integer-order counterpart, and it could be concluded that the fractional-order DVA has superiority in vibration engineering, and fractional-order element could replace the traditional damper and spring simultaneously in some cases.