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研究生:洪肇隆
研究生(外文):Hung,Chao-Lung
論文名稱:利用等效質量法來計算攜帶多個三自由度彈簧-質量系統之長方形板的自由振動特性
論文名稱(外文):Use of Equivalent-Mass Method for calculating the free vibration characteristics of a rectangular plate carrying multiple three degree-of-freedom spring-mass systems
指導教授:吳佳璋教授
指導教授(外文):Wu,Jia-Jang
學位類別:碩士
校院名稱:國立高雄海洋科技大學
系所名稱:輪機工程研究所
學門:工程學門
學類:機械工程學類
論文種類:學術論文
論文出版年:2010
畢業學年度:98
語文別:中文
論文頁數:38
中文關鍵詞:長方形板三自由度彈簧-質量系統等效質量法有限元素法自然頻率
外文關鍵詞:rectangular plate3-dof spring-mass systemequivalent mass methodfinite element methodnatural frequency
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  本文的主要目的在於提出一種利用一組等效質量來取代三自由度彈簧-質量系統的方法(本文稱之為等效質量法,Equivalent-Mass Method,EMM),因此,攜帶多個三自由度彈簧-質量系統之長方形板的自由振動特性便可由一攜帶相同組數之等效質量的長方形板的自由振動特性來預測。彈簧-質量系統之三個自由度的動態效應已經考慮在等效質量中,因此,對等效質量法而言,整體振動系統的自由度總數並不會隨著附加至長方形板之三自由度彈簧-質量系統總個數的增加而增加。然而,對傳統有限元素法(Finite Element Method,FEM)而言,多附加一個三自由度彈簧-質量系統至長方形板,則整體振動系統的自由度總數會增加3個。在比較等效質量法與有限元素法後,可以發現等效質量法有下列兩個優點:(1) 等效質量法所需要的自由度總數較少,因此,可節省一些電腦儲存記憶體;(2) 由於彈簧-質量系統之三個自由度的動態效應已經考慮在等效質量法中,因此,和彈簧-質量系統相關的結構局部自然頻率與振態也將移除,這可節省一些計算上述相關輸出資料的電腦時間。很明顯的,附加至長方形板之三自由度彈簧-質量系統總個數愈多,等效質量法的優點將愈顯著。
  This paper aims at presenting a technique to replace each three-degree-of-freedom (3-dof) spring-mass system (or substructure) by a set of equivalent masses so that the dynamic characteristics of a rectangular plate (or main structure) carrying any number of elastically mounted lumped masses may be obtained from the same plate carrying the same sets of rigidly attached equivalent masses. Because the three degrees of freedom (dof’s) of the substructure are embedded in its equivalent masses, the total dof of the entire vibrating system (i.e, the main structure together with all the substructures) is independent on the total number of the substructures attached to the main structure in the presented equivalent mass method (EMM). However, in the conventional finite element method (FEM), the total dof of the entire vibrating system increases by three when one more substructure is attached to the main structure. Compared with FEM, the merits of EMM are double: Firstly, since the total dof of the entire vibrating system in EMM is smaller than that in FEM, some computer storage memory may be saved. Secondly, since the dof’s for all the substructures are eliminated, the associated natural frequencies and mode shapes are excluded from those of the main structure and some effort required for the analysis of computer-output data may also be saved. It is evident that the last merits of EMM will be more predominant if the total number of substructures attached to the main structure is large.
目錄
封面……………………………………………………………………………
書名頁…………………………………………………………………………
授權書…………………………………………………………………………
審定書…………………………………………………………………………
摘要……………………………………………………………………………I
Abstract………………………………………………………………………II
謝誌…………………………………………………………………………III
目錄…………………………………………………………………………IⅤ
表目錄………………………………………………………………………ⅤI
圖目錄……………………………………………………………………ⅤII
符號說明……………………………………………………………………IX
第一章 前言………………………………………………………………1
  1.1 文獻回顧…………………………………………………………1
  1.2 論文架構…………………………………………………………4
第二章 三自由度彈簧-質量系統的等效質量…………………………5
  2.1 三自由度彈簧-質量系統的有效質量矩陣……………………5
  2.2 三自由度彈簧-質量系統的等效質量………………………10
  2.3 三自由度彈簧-質量系統的元素特性矩陣…………………11
第三章 負載板的自然頻率與振態………………………………………14
  3.1 三自由度彈簧-質量系統的有效質量矩陣…………………14
  3.2 等效質量法(EMM) ……………………………………………15
  3.3 有限元素法(FEM) ……………………………………………17
第四章 數值結果與討論…………………………………………………18
  4.1 可靠性驗證……………………………………………………18
  4.2 彈簧勁度的影響………………………………………………22
  4.3 質量和慣性矩的影響…………………………………………30
  4.4 攜帶四個完全相同之三自由度彈簧-質量系統的SFSF負載板…………………………………………………………………32
第五章 結論………………………………………………………………36
參考文獻……………………………………………………………………37
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3.Avalos, D.R., Larrondo, H.A., Laura, P.A.A., 1994. Transverse vibrations of a circular plate carrying an elastically mounted concentrated mass. Journal of Sound and Vibration 177, 251-258.
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11.Shah, A.H., Datta, S.K., 1969. Normal vibration of a rectangular plate with attached mass. Journal of Applied Mechanics 36, 130-131.
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13.Wu, J.S., Luo, S.S., 1997a. Use of the analytical-and-numerical-combined method in the free vibration analysis of a rectangular plate with any number of point masses and translational springs. Journal of Sound and Vibration 200, 179-194.
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