Active Control of Mechanical Vibration by the use of Fractional Calculus

Abstract

For the dynamics described by an equation of motion including fractional-order-derivative terms, the fractional-order-derivative responses cannot be measured directly through experiments. In the present study, three solutions are proposed that enable the fractional-order-derivative responses to be measured by a combination of signals obtained by existing sensors. Specialized sensors or complicated signal processing are not necessary. Fractional-order-derivative responses at a certain point on a structure can be expressed through linear combinations of the displacement signal and the velocity signal at each point on the structure.