Abstract:

This paper is essentially addressed to the vibrations of ships which were extensively studied both experimentally and analytically by modeling a ship as a beam of uniform cross section and predicting its vibration characteristics by Euler's theory of elastic beams. To begin with, the free vibration characteristics of a ship beam are predicted from Timoshenko's theory of elastic beam of variable cross section by use of Galerkin's method. The results are evaluated by use of those obtained recently from Euler's theory [e.g., S. Abrate, J. Sound. Vib. 185 (4), 703--716 (1995)]. Next, a numerical algorithm that is based on the method of moments [e.g., G. A. Altary and M. C. Dokmeci, Z. angew. Math. Mech. 77, 1--17 (1997) and references therein] is developed so as to predict the vibration characteristics of a ship beam at both low and high frequencies. The equations derived include the effects of warping and shear deformations of cross section and, in fact, they incorporate as many higher order effects as deemed necessary in any case of interest. They govern all the extensional, flexural, and torsional as well as coupled motions of ship beam. Also, the results are compared with those of earlier ones. [Work supported in part by TUBA.]