| Summary: | 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
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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.
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