由於跨徑之增加與整體質量輕量化之影響下，大跨徑屋頂結構的結構行為變的更複雜，對風的敏感度亦提高。台灣地處亞熱帶上的一個島國，時常會遭受到颱風的侵襲，因此其設計便不再只考慮地震力，更不能忽視其抗風分析。 本論文的研究主要是依據採用POD法獲得外力載重，和傳統Ritz向量疊加法相結合，計算結構的動態反應，並將其計算結果和直接積分，還有傳統動力模態疊加法(Modal dynamic)之結果相比較，來展現使用Ritz法求解的有效性和縮短計算時間的優點，以圓球網殼結構和苗栗巨蛋體育館作為此分析方法之研究對象。 由本文分析結果得知，利用POD法分解風力歷時資料，只需較少的前幾階特徵模態，便可很好的描述風場的特性。並以POD為外力結合Ritz向量的作法具有良好的計算精度和計算效率。此方法依據少量的Ritz向量便可得到較準確的風力反應，而且其計算時間遠小於直接積分法，也較傳統動力模態疊加法來的快速。 Due to the increase of span length and the reduction of total structural mass, the structural behavior of long span roof structure become more complicated. The sensitivity to wind for this type of structure is also increased. Because Taiwan is a typhoon prone area, the importance of wind resistant design of the type of structures can not be ignored. The main purpose of this thesis is to develop a method combined POD and Ritz vectors for improving the efficiency of calculations in the dynamic analysis of the long span roof structures under wind excitations. The numerical results obtained from this approach are compared with those obtained from direct integration and traditional modal analysis. Two examples are used to demonstrate the validity and the efficiency of this method. It can be inspected from the results that using a few POD modes and Ritz vectors can obtain satisfactory results efficiently. It is shown that this approach can save a lot of calculation time and still maintain the validity in both two examples. A parametric analysis including number of POD modes and number of Ritz vectors adopted in the analysis is also performed.
