由於薄壁曲樑的幾何性質之特殊，因此考慮各方向之剪切變形效應，轉動慣量效應、軸向慣量效應與軸向扭轉效應，如此方能推導得完整之薄壁曲樑運動方程式，本文分成兩個部分做討論，前半段利用樑的特性作中空曲樑的探討，而後半段是利用薄板元素堆疊中空樑導入板元素的特性作探討。
前半段結構的模態頻率值之探討，將具有矩形截面的中空曲形樑結構分成in-plane及out-of-plane兩方面；後半段利用薄板結構組合形成直線型薄壁樑探討其模態頻率值及比較單純薄壁樑之情形。
研究方法分為模態分析法與有限元素法。在模態分析法中，利用分離變數法，再代入邊界條件，可求得模態頻率值；對於利用有限元素法，則推導出形狀函數組，並選取不同元素數來堆疊樑結構；最後比較模態分析法與有限元素法分別所求得模態頻率值之相對誤差非常小。

In this thesis, the vibration of either a curved thin-walled beam with a closed rectangular cross-section or a straight box beam is investigated. The displacement and rotation angles along three principle axes of both two structures are considered. The warping effect in the contour of both two beams also is considered. Further, the thickness warping effect in the box beam is included. An analytic method is presented to investigate the effects of geometric parameters on the modal frequencies for the in-plane motion and the out-of-plane motion of both two structures. Further, the finite element technique also is presented in computing the modal frequencies of the two structure. Modal frequencies obtained from both two approaches are compared.

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