Transverse Vibrations of a Ship Hull in Ideal Fluid, Determined Through Variational Methods

Abstract

A direct formulation for analyzing the vibration characteristics of an arbitrary body and predicting the three-dimensional velocity potential is presented. It consists of forming the Lagrangian for a Timoshenko-beam fluid system and minimizing Hamilton's principal function by the Rayleigh-Ritz method. Due to the boundary condition, the minimizing sequence for vibration amplitude transforms the velocity potential into an associated sequence of Neumann boundary-value functions. These are expressed further in terms of another minimizing sequence and evaluated after minimizing the corresponding energy functionals according to the method of minimal surface integrals. The theory is applied to a simple body and the resulting vibration characteristics are found to be more accurate than previous theoretical estimates and closer to published experimental data. Finally, the feasibility of the procedure is outlined for a submerged ship hull, employing approximate methods of numerical quadrature.