Theoretical Analysis of Vibration Motion of Rectangular Thin Plate Immersed in Fluids

• Main Authors: Hsueh-Wei Hsu, 徐雪維
• Other Authors: Chien-Ching Ma
• Format: Others
• Language: zh-TW
• Published: 2015
• Online Access: http://ndltd.ncl.edu.tw/handle/00047988095207347268

碩士 === 國立臺灣大學 === 機械工程學研究所 === 103 === Fluid-structure interaction problem of vibration of fluid-coupled plates have received a great attention because of their importance in various engineering applications. A theoretical method is developed to investigate free vibration of rectangular thin plates immersed in fluids. Beam method is applied to construct mode shapes of a rectangular plate. The fluid is assumed incompressible and inviscid so that the fluid field could be expressed by velocity potential. Galerkin method is used to deal with the boundary conditions on the interface. At last, Rayleigh-Ritz method is applied to obtain the resonant frequency and mode shape of the rectangular plate immersed in fluid. The different boundary conditions of rectangular plate discussed in the study include fully clamped, free, and cantilever plate. A commercial finite element method (FEM) software is used to be compared with the theoretical analysis for checking the accuracy and suitable applied range of the theory. After confirming the accuracy and suitable applied range of the theoretical method applied on rectangular plate in air, that applied on rectangular plate which in contact with fluid on single side was also confirmed. Then, convergence test of theoretical method applied on rectangular plate immersed in fluid field with several different size was conducted to decide tolerance of numerical error. The resulting resonant frequencies and mode shapes was compared to FEM to confirm its accuracy and suitable applied range, too. The theoretical method was also used to solve stress field on the rectangular plate. Finally, the theoretical method was used to discuss the effect on the resonant frequency of the rectangular plate due to depth of fluid, position iv of rectangular plate in the fluid field and density of fluid and present the pressure and velocity of the fluid fields with different size coupled with the rectangular plate.