A simple and accurate added mass model for hydrodynamic fluid—Structure interaction analysis

A theoretical model of an added mass representation for a flexible cylinder vibrating in a fluid medium is presented. To accomplish this, the fluid-structure interaction problem under the influence of harmonic ground and inertia dominated hydrodynamic loading, is first studied by solving the coupled differential equations exactly. Explicit expressions for computing the hydrodynamic interaction pressure and eigenquantities like natural frequencies and mode shapes are given here. However, this analytical model, as in many other mathematical models, suffers from a severe handicap; its expressions are too complicated and require the use of a computer program to generate the results. One solution which is of particular interest, is the computation of natural frequencies. Using the added mass representation, a simple formula for evaluating the natural frequency is proposed. The formula is very simple to use, requiring only a minimal computational effort on a standard calculator. Comparison with the analytical solutions shows that the formula is extremely accurate, with errors under 0.5% or less, in nearly all the cases tested. Also, more importantly, this accuracy does not appear to deteriorate in the computation of higher natural frequencies, and thus should be very useful for designers working in the dynamics of submerged structures, taking into account their hydrodynamic interactions.