A structural modeling of torsional ship motions

Abstract

This study is concerned with a structural modeling for torsional motions of thin-walled girders of ships by beam idealization on the basis of three-dimensional theory of elastodynamics. In the modeling, (1) the fundamental equations of elastodynamics are expressed in a unified variational form that is expressed by means of Hamilton's principle through Friedrichs's transformation [M. C. Dökmeci, IEEE Trans. UFFC-37, 369–385 (1990)]. Next, (2) a series representation in the aerial coordinates of cross section is introduced for the displacement field. Mindlin's averaging procedure in the variational form is used so as to derive the one-dimensional governing equations of torsional motions. The governing equations that are expressed both in local and variational forms incorporate all the significant effects of motion; the warping of cross section, the geometrical nonlinearity, and the fluid effect by the added mass concept of ship are all taken into account. Further, (3) special cases are discussed and, in particular, the fully linearized governing equations are studied. The sufficient conditions are enumerated for a unique solution of the linearized governing equations by use of the logarithmic convexity argument.