Damped Oscillator under Stokesian Realm and Added-Mass Effects

Abstract

This article presents the modeling and simulations of a sphere that oscillates vertically in a high-viscosity liquid. The sphere is connected to a linear spring and given an initial displacement from the equilibrium position to allow free vibration and the sphere undergoes the inertia force, the spring force, the drag force, the buoyancy force, the gravity force, and the added-mass force. In general, the added-mass force is not considered in modeling an oscillator. In this article, the added-mass force is included in the modeling to reflect the reality and the effect of the added-mass force is investigated and discussed. The main contribution of this article is to model and simulate the system and to show that i) the natural frequency of oscillation is reduced by the added mass; ii) the damping ratio is also reduced by the added mass; iii) the return time to the original equilibrium is increased by the added mass; iv) furthermore, the difference on the densities between the liquid’s density and the sphere’s density dictates the degree of the added-mass effect; i.e., the effect due to the added mass is small if the difference on the densities is large.