工學院: 機械工程學研究所指導教授: 馬劍清徐雪維Hsu, Hsueh-WeiHsueh-WeiHsu2017-03-132018-06-282017-03-132018-06-282015http://ntur.lib.ntu.edu.tw//handle/246246/278475流-固耦合之問題應用廣泛，且固體結構與流場耦合之振動行為受到重視。本 文主要探討長方形薄板在流-固耦合狀況下之振動問題。固體結構部分，以樑函數 建構長方形薄板之振動模態。流體方面假設流體為無黏滯性、不可壓縮，則流場 可以速度勢能表示。以離散法處理流-固耦合介面上之邊界條件，最後使用瑞雷- 瑞茲法求得此流-固耦合系統中長方形板之共振頻率及共振模態。 本文以商用有限元素分析軟體計算結果做為對照，驗證理論分析之準確性與 適用範圍。在確認分析方法應用於空氣中振動之全固定、全自由以及懸臂之長方 形板之振動問題的可行性之後，對於單側接觸流場之全固定、全自由以及懸臂之 長方形板振動問題之理論分析結果的可行性做確認。接著再討論完全浸泡於流場 中之全固定、全自由以及懸臂之長方形板的振動問題，對其分析結果做收斂分析， 再將理論分析求得之共振頻率、共振模態與有限元素分析軟體之計算結果加以比 對，釐清此方法存在之數值誤差與此方法之適用範圍。此外，也將理論應用於求 解長方形板上之應力場。最後應用理論分析探討流-固耦合問題中液體之深度、液 體之密度、長方形薄板之垂直位置與水平位置與長方形薄板振動特性之關係並且 討論流-固耦合問題中長方形薄板的振動對於不同大小之流場之壓力、流速之影 響。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.20557801 bytesapplication/pdf論文公開時間: 2017/8/17論文使用權限: 同意無償授權流-固耦合振動共振頻率共振模態fluid-structure interactionresonant frequencyvibrationmode shapethesishttp://ntur.lib.ntu.edu.tw/bitstream/246246/278475/1/ntu-104-R02522501-1.pdf