Analytic solution to the coupled vibration characteristics of a rectangular plate partially immersed in a finite fluid container

The objective of this study was to explore from a theoretical perspective the relationship between dry mode shapes and the distortions associated with wet mode shapes. This study investigated the free vibration characteristics of a rectangular thin plate partially coupled with fluid. A powerful full-field experimental technique referred to as AF-ESPI was used to measure vibration modes and the corresponding resonant frequencies. The derivation of wet mode shapes from dry mode shapes proved effective in analyzing problems for plate-fluid interactions. Our analysis revealed that every wet mode shape is composed of multiple dry mode shapes with corresponding contribution coefficients. In the proposed analytic approach, the superposition method is used to deal with theoretical aspects of thin plate vibration behavior, and velocity potential is used to express the dynamic behavior of an incompressible flow field in a finite container. The accuracy of the results obtained using the proposed theoretical approach was verified via comparison with numerical results obtained using finite element method (FEM) and experimental measurements. A detailed discussion pertaining to the relationship between wet and dry mode shapes is also presented.