臺灣博碩士論文加值系統

工程上板構件常會面臨應力奇異點(stress singularity)之問題，造成的原因之一有幾何不連續。當數值分析含奇異點之結構單元時，該奇異點之特性須被正確之模擬，方能得到準確之解。本論文將使用Ritz法，並引入描述彎矩與剪力奇異性之角函數(corner function)於完備允許函數序列中，用以求取含有奇異點厚板之自然振動頻率。文中的研究案例為懸臂扇形板及斜形板，探討漸近解加速板振動自然頻率解收斂之特性，以及探討不同幾何參數(例如扇形板之徑厚比(a/h)、扇形角(α)及斜角，及斜形板之長寬比(a/b))對板振動自然頻率之影響。詳細的數值分析顯示在完備允許函數序列中加入角函數能夠加速頻率之收斂性，且隨著扇形角或斜角角度的增加，角函數的引用顯得更重要。

The stress singularities in a plate often occur in engineering practices, which may be due to the irregular geometry of plate. The stress singularity behaviors must be exactly described in a numerical analysis to obtain an accurate solution. This work applied the Ritz method to determine the vibration frequencies of Mindlin plates, and introduces the asymptotic solutions exactly describing the singularity of bending moment and shear forces into a complete set of admissible functions. The cases studies consist of cantilevered sectorial plates and cantilevered skew plates, in which we also investigate the vibration behaviors affected by geometry parameters, namely thick-to-radius ratio and opening angle in a sectorial plate or skew angle and aspect ratio in a skew plate. Convergence studies show that corner functions do enhance the convergence rate of the frequencies. Including corner functions in the admissible functions is getting more important as the sectorial angle or skew angle increases .

目 錄
中文摘要 i
英文摘要 ii
誌謝 iii
目錄 iv
表目錄 vi
圖目錄 viii
第一章 緒論 1
1.1 研究動機與方法 1
1.2 文獻回顧 2
1.3 內容概要 4
第二章 奇異漸近解之推導 6
2.1 基本公式 6
2.2 彎矩奇異性之漸近解 8
2.3 剪力奇異性之漸近解 14
第三章 扇形板之振動分析 18
3.1 Mindlin板之應變能與動能 18
3.2 以Ritz法求取自然振動頻率 19
3.3 允許函數 22
3.4 收斂性分析 25
3.5 數值分析 29
第四章 斜形板之振動分析 31
4.1 Mindlin板之應變能與動能 31
4.2 以Ritz法求取自然振動頻率 33
4.3 允許函數 35
4.4 收斂性分析 37
4.5 數值分析 40
第五章 結論與建議 42
5.1 結論 42
5.2 建議 43
參考文獻 44

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林聰悟，林佳慧，西元1999年，「數值方法與程式」，圖文技術服務有限公司。