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題 名 | An Analytical Solution for Out-of-plane Vibrations of an Arch with Variable Curvature=變曲率拱面外振動之解析解 |
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作 者 | 黃炯憲; 曾一平; 張書豪; | 書刊名 | 力學 |
卷 期 | 13:4 1997.12[民86.12] |
頁 次 | 頁349-361 |
分類號 | 440.2 |
關鍵詞 | 解析解; 動態勁度矩陣; 面外自由振動; 變曲率拱; Analytical solution; Dynamics stiffness matrix; Out-of-plane free vibration; Variable curvature arch; |
語 文 | 英文(English) |
英文摘要 | 本文利用Frobenius 法 結合動態勁度法推導變曲率拱面外振動之解析解。此解 考慮了撓曲、扭曲、及剪力變形,和旋轉慣性。此解析解可保證得到收斂解而不會遇到任 何數值問題。此解之重要副產品為首次提供了變曲率拱面外振動之動態勁度矩陣;因此,此 解可輕易地結合其他桿件元素之動態勁度矩陣進行更複雜結構系統如拱橋之精確動力分析。 利用所得之解析解,本文針對橢圓拱進行一系列之分析並以圖表表示之,以填補文獻之不足 。最後,本文亦對一完整橢圓環和斷裂橢圓環之動力特性加以分析討論。 n important by-product of this analytical solution is that the first known dynamic stiffness matrix for an arch with variable curvature is also explicitly formulated, which has great potential for further application on accurately analyzing the dynamic responses of a complex system like arch bridge or a space frame consisting of curved beams with variable curvature. By applying the proposed solution, three subjects have been comprehensively studied to fill voids in the vibration literature. Extensive non-dimensional frequencies of elliptic arches with various opening angles are shown in graphic charts. The effects of the shapes of cross-section on the natural frequencies of elliptic arches are also investigated. Finally, the dynamic behaviors of elliptical rings with and without a cut are studied. |
本系統中英文摘要資訊取自各篇刊載內容。