Dynamics of elastic ship laminae

Abstract

This paper is addressed to the macromechanical analysis of dynamics of an elastic ship laminae within the effective stiffness concept of composites. The laminae that may possess arbitrary number of layers is immersed within an ideal fluid of infinite extent. In the first part, a variational principle [N. Sarigül and M. C. Dökmeci, AIAA J. 20, 1173–1175 (1984)] is extended by Friedrichs's transformation [M. C. Dökmeci, IEEE Trans. UFFC-35, 775–787 (1988)] so as to formulate a unified variational principle of fluid-solid interaction. In the second part, a set of two-dimensional governing equations of laminae is systematically derived by means of a variational principle together with a series representation in the thickness coordinate for the fields of displacement and hydrodynamic pressure that are chosen as a basis of derivation. The significant effects of laminated composites are considered, including those of the dynamic interactions between, and the hydrodynamic pressure on, the layers. The governing equations accommodate all the types of motions of laminae. In the third part, emphasis is placed upon a theorem of uniqueness in solutions of the governing equations and special cases.