工學院: 機械工程學研究所指導教授: 馬劍清紀明Ji, MingMingJi2017-03-132018-06-282017-03-132018-06-282015http://ntur.lib.ntu.edu.tw//handle/246246/278370本文主要首先以Reddy板理論及Leissa板理論解析橫向等向性圓板的三維振動特性的問題，接著利用Reddy板理論及Leissa板理論解析壓電圓形厚板三維振動特性問題。本文首先利用漢密爾頓原理推導出橫向等向性圓板以面外振動為主和以面內振動為主的統御方程式及邊界條件，於邊界條件上的探討，本文討論自由邊界與固定邊界兩種不同的邊界條件，並且分別求出面外振動為主和面內振動為主的共振頻率、模態振形，並對比有限元素法之結果驗證理論之正確性；接著本文提出四階電位假設形式與二階電位假設形式，並且利用漢密爾頓原理推導出壓電圓形厚板以面外振動為主和以面內振動為主的統御方程式及邊界條件，並對比有限元素法之結果以驗證理論之正確與否。研究結果表明，本文所用的Reddy板理論及Leissa板理論適用於解析橫向等向性圓板和壓電圓形厚板三維振動特性的問題。This paper presents the free vibration analyses of transversely isotropic circular plate and piezoelectric circular plate based on Reddy plate theory and Leissa plate theory. Governing equations and boundary conditions of transversely isotropic circular plate are derived from Hamilton’s principle.To validate the plate theories, the resonant frequencies and mode shapes of in-plane and out-of-plane vibrations are compared with those obtained from finite element analysis.Then the higher order plate theories are employed to obtain results of free vibrations for piezoelectric circular plates.The results of theoretical analyses are in good agreements with the results of numerical analyses. Finally,the two complete theories,Reddy plate theory and Leissa plate theory,which are useful and accurate are developed for establishing free vibration frequencies and mode shapes.192613214 bytesapplication/pdf論文公開時間: 2017/8/21論文使用權限: 同意無償授權Reddy板理論Leissa板理論橫向各向同性圓板壓電圓板共振頻率模態振形Reddy plate theoryLeissa plate theorytransversely isotropic circular platepiezoelectric circular plateresonant frequenciesmode shapesthesishttp://ntur.lib.ntu.edu.tw/bitstream/246246/278370/1/ntu-104-R02522537-1.pdf