Analytical solution for the vibration characteristics of a partially immersed plate with experimental investigation on wet mode shapes

The objective of this paper was to investigate the relationship between dry mode shapes and the distortions associated with wet mode shapes base on theoretical analysis. The superposition method was used to construct the theoretical results of vibration behavior for cantilever plates. Flow field pressure was derived using an equation governing the behavior of incompressible fluids in a finite container. Analytic solutions for vibrations in a cantilever plate in air served as the fundamental function of the thin plate partially immersed in the liquid. We then used fluid pressure, and the deflection of the thin plate for the construction of frequency response functions for the analysis of vibration characteristics in the fluid-plate coupling system. Two powerful experimental measuring methods referred to as amplitude-fluctuation electronic speckle pattern interferometry (AF-ESPI) and the fiber Bragg grating (FBG) sensor were used to measure the resonant frequencies and wet mode shapes. A detailed investigation on the distortion phenomena of cantilever plate with different levels of submergence is presented. Effects of a solid wall on the vibrating plate are also discussed by the experimental measurement and theoretical analysis. Comparison of the results from theoretical analysis, finite element method, and experimental measurements confirmed the accuracy of our theoretical analysis. Our methodology provided an intuitive method to discuss the distortion phenomena of partially submerged plates based on the relationship between dry and wet mode shapes.