Oscillatory tests were performed on several geometric shapes in the vicinity of' the free surface of an undisturbed fluid. The tests, together with an accompanying literature review, were conducted to determine the influence of geometry, depth, amplitude of motion, and frequency on the fluid added mass and damping coefficients.

The results, which are in broad agreement with the theoretical calculations, are used to generate empirical expressions for a range of frequencies, depths, and geometries.


In this paper we are addressing the problem of determining the added mass and the damping coefficients for submerged bodies oscillating near the surface. Why are these parameters of interest. Because they influence the motions and loads of all bodies subjected to the dynamic forces of the sea.

The expansion of' offshore and undersea operations has resulted in many new technological problems, among them the design of structures to withstand and operate in ocean waves. Typical areas of interest include:

  • Motions of drilling ships

  • Motions and loads in semi-submersibles

  • Dynamics and loads of' mooring systems

  • Dynamics and loads of towing systems

  • wads in stationary offshore structures

  • Dynamics and loads of submerged systems

The successful design of these systems requires knowledge of wave-induced loads and motions. But to determine these we must know the system transfer functions for prescribed wave heights, periods, spectral distributions, etc. The transfer functions depend principally on configuration geometry, and mass, damping and stiffness coefficients. Mass and damping coefficients are difficult to determine because they are affected by so many parameters (e.g. configuration, proximity to the surface, frequency and amplitude of oscillation, fluid properties, etc.) Because of this difficulty, model tests are often reliedon to study design adequacy. For some applications, model test alone is adequate. However, analysis is needed to study the effects of conditions which cannot be duplicated in test tanks (for example, directional sea spectra and multiple swells). Even more important, analysis is needed to optimize the design. With the increasing importance of safety, depth capabilities, operating in rough seas, cost reductions, etc., design optimization is often essential.

The following sections discuss added mass and damping, and review some of the techniques for using these coefficients for analyzing dynamic motions. In addition, we discuss values of added mass and damping calculated in the literature and, finally, present the results of tests conducted on simple geometric shapes.

Methods Of Analyzing Structubal Responses To Waves
Simple Structures

For spherical, cylindrical, ellipsoidal, other simple configurations a number of authors (See Refs. 1-6) have obtained mathematical solutions for the fluid pressures resulting from harmonic motions of the structure. Few, however, - this paper included have obtained fluid pressures for harmonic motions of the fluid, such as that produced by waves. In this paper we shall refer to the former as "hydrodynamic" pressures and the latter as "virtual" pressures.

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