Experimental Investigation of Fractional Order Behavior in an Oscillating Disk

Abstract

Abstract An experimental investigation is presented of an oscillating disk submerged in water. The system is adapted from one modeled by the Bagley-Torvik equation, being modified to more closely approximate idealizations in the derivation. The modified system eliminates alignment problems that would violate the assumption of fluid forces being due only to shear in the fluid. An implicit finite difference model based on the Riemann-Liouville fractional derivative was used to model the observed oscillatory free response resulting from a non-homogeneous initial condition. The numerical model accounted for motion well until the amplitude was small.