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研究生:何國輝
研究生(外文):Ho Kuo Huei
論文名稱:不同板理論徑向簡支扇形板之振動理論解
論文名稱(外文):Analytical solution for sectorial plateswith simply-supported radial edges based on various plate theories
指導教授:黃炯憲黃炯憲引用關係
學位類別:碩士
校院名稱:國立交通大學
系所名稱:土木工程系
學門:工程學門
學類:土木工程學類
論文種類:學術論文
論文出版年:2002
畢業學年度:90
語文別:中文
論文頁數:128
中文關鍵詞:解析解極正向性材料Mindlin扇形板Reddy扇形板振動
外文關鍵詞:analytical solutionpolarly orthotropic materialMindlin sectorial plateReddy sectorial platevibration
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本文分別推導極正向性之古典扇行板、Mindlin扇行板和Reddy扇行板之振動理論解,並探討側向剪力變形對扇行板振動之影響。其理論解乃利用Frobenius方法並滿足徑向、環向邊界條件及兩徑向邊之頂點處的正規條件所建構之級數解。
在兩徑向邊之頂點處,藉由力與位移之關係可發現彎矩或剪力有可能趨近無限大,因而造成彎矩奇異性及剪力其異性。本文所建構級數解之精確性可將正向性扇行板簡化為等向性扇行板,並求出無因次化頻率與目前文獻之閉合解比較,可得驗證。
另外本文也分別探討在環向自由端或固定端下,彈性模數及剪力模數對扇行板振動頻率之影響。此外本文也列出改變彈性模數及剪力模數,彎矩奇異和剪力奇異隨著扇行角變化的結果。

This thesis presents the first known analytical solutions for vibrations of a polarly orthotropic sectorial plate with simply-supported radial edges based on the Classical plate theory, Mindlin plate theory and Reddy plate theory. These solutions are series solutions constructed using the Frobenius method and exactly satisfy not only the boundary conditions along the radial and circular edges, but also the regularity conditions at the vertex of radial edges. The moment or shear force singularity at the vertex are exactly considered in these solutions. The correctness of these proposed solutions is confirmed by comparing nondimensional frequencies of isotropic plates obtained from the present solutions corresponding to different plate theories with published data obtained from closed form solutions. This thesis also investigates the effects of elastic and shear moduli on the vibration frequencies of the sectorial plates with free or fixed boundary condition along the circumferential edge. A study is also carried out about the influence of elastic and shear moduli on moment or shear force singularity at the plate origin (r=0) for different vertex angles.

目 錄
目錄
表目錄
圖目錄
第一章 緒論
1.1 前言
1.2 研究動機
1.3 文獻回顧
1.3.1 古典板理論
1.3.2 Mindlin板理論
1.3.3 Reddy厚板理論
1.4 內容概要
第二章 古典板理論解
2.1 古典板理論
2.1.1 位移場
2.1.2 應變-位移關係
2.1.3 應力-應變關係
2.1.4 力(stress resultant)與位移分量之關係
2.2 運動方程式
2.3 級數解
2.4 頻率方程式
2.5 收斂性分析
2.6 數值結果分析
2.7 奇異性分析
第三章 Mindlin板理論
3.1 Mindlin板理論
3.1.1 位移場
3.1.2 應變與位移關係
3.1.3 應力與應變關係
3.1.4 力(stress resultant)與位移分量之關係
3.1.5 Mindlin板之振動方程式
3.2 級數解
3.3 頻率方程式
3.4 收斂性分析
3.5 數值結果分析
3.6 奇異特性分析
第四章 Reddy板理論解
4.1 Reddy板理論
4.1.1 位移場
4.1.2 應變與位移關係
4.1.3 應力與應變關係
4.1.4 力(stress resultant)與位移分量之關係
4.1.5 Reddy板之運動方程式
4.2 級數解
4.3 頻率方程式
4.4 結果分析與討論
4.5 奇異特性分析
4.6 環狀扇型板之級數解
第五章 結論與建議
5.1 結論
5.2 建議
參考文獻
附錄A
附錄B
附表
附圖

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2. A. W. Leissa 1969, Vibration of Pates, NASA SP-160, U.S. Government Printing Office.
3. A.W. Leissa 1978, “Recent research in plate vibrations (1973-1976) “, Shock and Vibration Digest, 10(12), 21-35.
4. A. W. Leissa 1981, “Plate vibration research (1976-1980) “, Shock and Vibration Digest, 13(10), 19-36.
5. A. W. Leissa 1987, “Recent studies in plate vibrations: 1981-1985, part I: classical theory“, Shock and Vibration Digest, 19(2), 11-18.
6. A. W. Leissa 1987, “Recent studies in plate vibrations: 1981-1985, part II: complicating effects“, Shock and Vibration Digest, 19(3), 10-24.
7. M. Ben-Amoz 1959, “Note on deflections and flexural vibrations of clamped sectorial plates“, Journal of Applied Mechanics, ASME, 26(1), 136-137.
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10. K. Maruyama and O. Ichinomiya 1981, “Experimental investigation of free vibrations of clamped sector plates“, Journal of Sound and Vibration, 74(4), 563-573.
11. T. Irie, G. Yamada, and F. Ito 1979, “Free vibration of polar-orthotropic sector plates“, Journal of Sound and Vibration, 67(1), 89-100.
12. C. Rubin 1975, “Vibrating modes for simply supported polar-orthotropic sector plates“, Journal of Acoustic Society of American, 58(4), 841-845.
13. C. S. Huang, A. W. Leissa, and O. G. McGee 1993, “Vibrations of sectorial plates having corner stress singularities“, Journal of Applied Mechanics, ASME, 60, 134-140.
14. R. D. Mindlin and H. Deresiewicz 1954, “Thickness-shear and flexural vibrations of a circular disk“, Journal of Applied Physics, 25, 1329-1332.
15. P. R. Benson and E. Hinton 1976, “A thick finite strip solution for static, free vibration at stability problems”, International Journal for Numerical Methods in Engineering, 10, 665-678.
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17. R. S. Srinivasan and V. Thiruvenkatachari 1985 , “Free vibration of transverse isotropic annular sector Mindlin plates“, Journal of Sound and Vibration, 101(2), 193-210.
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23. E. Kreyszig 1993, “Advanced Engineering Mathematics“, John Wiley & Sons, INC.
24. 錢偉長,「彈性力學」,亞東出版社,民國八十年。

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