- 學位論文
混合型質量矩陣對桿元素自然頻率之影響
Influence on mixing type of quality matrix to the natural frequency of bar element
摘要
有限元素法求取桿的自然頻率，其質量矩陣有Lump-Mass Matrix 、Consistent-Mass Matrix與混合質量矩陣。在以往的文獻中，混合質量矩陣為Lump-Mass Matrix 與Consistent-Mass Matrix 的平均值，也就是混合參數α=0.5。而自然頻率的準確性與桿的元素數目相關，然而太多的元素數目造成計算的不便。本研究利用調整混合參數的混合質量矩陣，來簡化有限元素的數目，提高有限元素的方便性，並能維持良好的準確度。 本研究發現，對第一模態與第二模態的自然頻率而言，α=0.5的混合參數，必須要有3個(第一模態)與6個(第二模態)以上的元素，其準確度較佳，針對第一模態而言，只取一個元素，其α=0.43171，其結果有很好的準確性，針對第二模態而言，只取2個元素時，α=0.3234，其結果有很好的準確性，本研究亦提出混合參數與元素數目的關係式，以供工程師參考。
並列摘要
From the rule of the limited element to get figures replies to the natural frequency of the bar, its quality matrix is Lump-Mass Matrix, Consistent-Mass Matrix and mixed quality matrix. From many reports reported, The figures of mix quality matrix is the averages of Lump-Mass Matrix and Consistent-Mass Matrix to mix quality matrix, that is to say that mixing parameter α =0.5. And natural accuracy of frequency correlate with figure of element of the bar, but too many element figure cause calculate inconvenient. This research utilizes and adjusts and mixes mixing quality matrix of the parameter, to simplify the figure of the limited element, improve the convenience of the limited element, and to maintain good accuracy. After our researched to find out, as to first mode and the second modal natural frequency, α = 0.5(mixing parameter), there must be over 3 elements of the first mode and 6 elements of the second mode , the result is accurate, regarding first mode, only catch an element, for α =0.43171, its result has very good accuracy, regarding second mode, while only catch 2 elements, α =0.3234, its result has very good accuracy, For engineer's reference this research also provide the relative expression of mixing the parameter and figure of element.