Viscous Damping: Time Convolution of Impulsive Solution

Abstract

A method is proposed to calculate the interaction between an oscillating body and the water surrounding it for low values of the Keulegan‐Carpenter number and in laminar flow conditions. Rather than dividing the viscous forces originated by the unsteady motion into an added mass inertia force and a frictional, energy dissipating, component, the interaction is here evaluated through a “Basset term” style convolution integral of the expression of the force calculated for impulsively started flow. A numerical procedure is employed to show that, for simple motions, the method herein proposed yields solutions similar to those obtainable by the classical approach, while it can efficiently deal with problems involving complex forcing actions or very short impulses, where the traditional approach fails to provide satisfactory results. The applicability of this technique is limited to purely laminar flows, thus including most of the problems related to the hydrodynamic damping of vibrating structures and excluding the whole domain of wave induced forces.