本文利用軸向束制的觀念來從事剛架的動力分析。首先先由剛架的基本資料來算出此剛架的獨立移動模態數目，再由原來的剛架去除結點抗轉動的內力，得到一類比於原來剛架的桁架結構，對此桁架的結構勁度矩陣，利用修改高斯消去法找到勁度最弱的結點及方向。令每一個最弱勁度點的移動量為一單位，加上每支桿件長度不變的束制條件，得到對應的移動模態向量。再對移動模態向量稍加修改，並補上結點轉動位移的影響，可得結構之變位諧和矩陣，然後依同餘轉換法，就可得到結構勁度矩陣，之後開始來從事動力的分析。利用振態疊加的觀念，將所得到的勁度矩陣來做振態分析，以得到我們所想要的結果。 軸向束制的應用，主要的目的可以減少自由度的數目，使得在分析時的運算時間可以更加的有效率。另外，在分析後可以得到一個近似的結果，適合使用在結構物的初步分析，來提升我們分析結構物時的實用性。 The concept of axial constraint is used in the dynamics analysis of frames in this paper. First, calculate the numbers of independent translation mode shapes of frame from the basis data. Then, the key procedure is using a modified structure with all rotational constraints removed from the original structure. We can find the joints of the weakest stiffness and its directions by using the method of modified Guass elimination. Let every translation of the weakest stiffness joint be one unit. And the condition of the constraint of the member length is not changed. Then, we get the correspondent translation mode shapes. More modification of the translation mode shapes and adding the effect of the joint rotation are done. We can get the compatibility matrix of the structure. By the congruent transformation method, the structural stiffness matrix is gained. Next, we can address the dynamics analysis by mode analysis method.
