Plate-fluid-interaction modeling and wet vibration analysis

Vibration of plate structures in air (dry) and in contact with fluid (wet) is of great interest and practical importance in naval architecture and marine applications. Therefore, a fundamental understanding of the natural vibration frequency and mode of various plate structures under different boundary conditions and environments is essential, especially for early-stage ship structural designs. In this paper, the dry and wet vibrations of simply supported rectangular Mindlin plates are studied with emphasis on developing closed-form solutions of vibration frequencies and quantification of uncertainties of different types. In plate-fluid-interaction modeling, potential flow assumption is adopted for the fluid, while orthotropic thick-plate condition is used for starting the plate bending formulation. The coupling between the fluid and plate is achieved through the fluid–plate interface, where the pressure is the same across the fluid–plate interfaces and the fluid–plate contact is permanent. Closed-form analytical solutions of added mass due to hydrodynamic effects of the potential fluid with several typical boundary conditions are presented first, and then the differential governing equations of orthotropic Mindlin plate with added mass considered are derived for the first time. Subsequently, simple solutions of wet vibration frequency are presented for both Mindlin plate and Kirchhoff–Love plate. With the derived closed-form solutions, parametric study and comparison between these two plate models can be easily conducted. For a given fluid–plate interaction model, the variations of the obtained vibration frequency are further evaluated with probabilistic analysis and Monte–Carlo simulation by considering the uncertainties and variations of the influencing parameters. This study sheds significant light on the fundamental plate-fluid-interaction in terms of wet vibration and provides potential opportunities for further development in ship structural reliability, noise and comfortness management, and the control of acoustic signatures.