Vibrations of Elastic Bottom Plate of A Sealed Rectangular Container Fully Filled With Liquid

The hydroelastic vibration of a rectangular plate, which is an elastic part of the rigid bottom of a sealed rectangular container fully filled with liquid, is studied. Both the vertical walls and the horizontal top of the container are rigid. An analytical-Ritz method is developed to analyze the dynamic behavior of the liquid-plate interaction. Firstly, the exact expression of velocity potential of the liquid is derived by the method of separation of variables. The unknown coefficients in the solution are determined by the liquid-plate interface condition in a form of integrals including the unknown dynamic deformation of the plate. Secondly, the total energy of the liquid-plate system is derived. Using Green's theorem, the volume integral of liquid kinetic energy is transformed into a surface integral surrounding the liquid domain. Thirdly, by expanding the wet modes of the plate into a series of beam vibrating functions and using the Ritz method, the eigenvalue equation of the liquid-plate system is obtained. Finally, the high accuracy and small computational effort are demonstrated by typical convergence studies. The effects of various parameters on eigenfrequencies of the liquid-plate system are discussed in detail.