A Simple Method for Calculating the Bending Modal Frequencies of an Underwater Simply Supported Beam with Hydrodynamic Study

摘要

A theoretical model of an added water mass representation for calculating the bending modal frequency of a simply supported beam in water medium is presented. To accomplish this, the explicit expressions for computing the hydrodynamic interaction pressure and forced transversal displacements are first derived, and the bending modal frequencies can be accurately obtained by searching the corresponding resonance frequencies. The validity of the analytical process is checked by the finite element method. As the complicated interaction between the structures and water can be approximated to added mass, if the beam is sufficiently slender. Using the added mass curves, a simple method for evaluating the bending modal frequency of an underwater simply supported beam is proposed, and an approximate formula is found subsequently. The comparisons between the analytical solution and the simple method show that the simple method is adequately accurate, with errors less than 1%, and both of the added mass curves and the approximate formula have nothing to do with different material attributes.