Hydrodynamic Mass Matrix for a Multibodied System

Abstract

A matrix technique is developed herein for generating the hydrodynamic mass matrix associated with a multimass system immersed in a liquid environment. The technique assumes that the liquid environment may be represented by a series of flow-channels and nodes. Flow-channels are introduced in the region between surfaces of neighboring solids, and nodes are used to connect two or more flow channels. It is assumed that the solid bodies undergo unidirectional motion and that potential flow theory is applicable. Equations for fluid flow in a variable area flow-channel are obtained by first developing the governing equations for fluid flow in a channel bounded by two parallel surfaces which may move in translation both perpendicular and parallel to the direction of flow. The continuity equation is then developed for an arbitrary node, and the general matrix equation for computing hydrodynamic mass obtained by applying the developed equations to a particular problem.