Sergey V. Sorokin
Dept. of Eng. Mech., Marine Tech. Univ., Lotsmanskaya str., 3, St. Petersburg, 190008, Russia
A problem of vibrations and sound radiation from laminated plates of finite length submerged in a fluid (acoustic medium) is formulated as a problem of optimal design width and of advanced materials. The parameters of design are the coefficients of the constitutive matrix for the plate's composite material. The sequence of constitutive laws is examined including the models for laminated plates with sharply different plies. Forced vibrations of plates of finite length are considered. Both the interaction between an acoustic medium and a plate and the interaction between a rigid (soft) acoustic baffle and a plate are described by boundary integral equations, which are assembled in a two-level system. The first level boundary equations govern the dynamics of a plate. They contain driving loads, unknown acoustic pressure, and the plate's boundary displacements and forces. The second level boundary equation describes the structural--acoustic interaction. The classical boundary equation related to contact acoustic pressure is modified by a substitution of a Somigliana's type formula for normal displacements of points of the plate's surface in contact with a fluid. Special attention is paid to the construction of Green's functions for vibrations of unbounded plates in the framework of various plate's theories. These Green's functions contain the parameters of design (elastic modules of materials of plies) in the explicit form. The asymptotic analysis of Green's functions for laminated plates is performed along with the asymptotic analysis of boundary equations. Based on these analyses some simplified models of fluid--laminated plate interaction are developed for certain bands of excitation. A semi-analytical sensitivity analysis of an energy flux and a directivity of radiation to the parameters of design is performed. The coefficients of constitutive matrices that mostly affect the fluid--structure interaction are revealed for the plate's theories considered. The ways of active control of vibrations and sound radiation by the regulation of material parameters of plies are discussed.