(3.238.96.184) 您好!臺灣時間:2021/05/18 15:09
字體大小: 字級放大   字級縮小   預設字形  
回查詢結果

詳目顯示:::

我願授權國圖
: 
twitterline
研究生:莊士德
研究生(外文):Chuang Shih Te
論文名稱:求解不均勻樑附帶彈簧─質量懸吊系統之自然頻率及振態之正解
指導教授:陳徳煒
指導教授(外文):Chen Der-Wei
學位類別:碩士
校院名稱:國防大學中正理工學院
系所名稱:造船工程研究所
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:2005
畢業學年度:93
語文別:中文
中文關鍵詞:彈簧 質量 系統 振態 頻率
相關次數:
  • 被引用被引用:0
  • 點閱點閱:98
  • 評分評分:
  • 下載下載:0
  • 收藏至我的研究室書目清單書目收藏:0
摘要

一附帶任意數量彈簧─質量懸吊系統的樑,假使其左端及右端的每個安裝點和樑的每一邊都被認為是節點,然後考量在相鄰接的兩個樑段的每個安裝點和結合每個彈簧─質量懸吊系統的力矩方程式之中變形的相容性和力平衡狀態,同時在 的方程式中可以得到v個附著點, 中之元素是在第v段和第 樑段的分割與在第v個彈簧的質量其相對應的模態位移之特徵函數的積分常數所組成的。那是相當顯而易見的,假使 考量到結位移向量,而 為在第v個附著點(聯合第v個和第 個樑段)的元素勁度矩陣。有鑑於最後的事實,透過考慮到整個樑的邊界條件,我們可以使用數值組合法為全部的附著點(組合全部的樑段)來取得有限元素法中所要使用的聯立方程式 。求解 (其中 代表行列式)可得受拘束樑(附帶數個彈簧─質量懸吊系統)其自然頻率的正解,並且將 的每一個相對應的值代入每一個附著點相關的特徵函數之中,就會決定其相對應的振態。目前並沒有採取類似
NAM的方法來求取此模型之自然頻率和相對應振態之正解。
ABSTRACT

For a beam carrying any number of spring-mass systems, if the left side and right side of each attaching point and each end of the beam are regarded as nodes, then considering the compatibility of deformations and the equilibrium of forces between the adjacent beam segments at each attaching point and incorporating with the equation of motion for each spring-mass system, a simultaneous equations of the form may be obtained for the v-th attaching point, where the elements of are composed of the integration constants for the eigenfunctions of the v-th and (v+1)-th beam segments and the associated modal displacements of the v-th sprung mass. It is evident that if is considered as the nodal displacement vector, then will be equivalent to the element stiffness matrix for the v-th attaching point (associated with the v-th and (v+1)-th beam segments). In view of the last fact, ome may use the numerical assembly method (NAM) for the conventional finite element method to obtain the simultaneous equations, , for the overall attaching points (associated with the overall beam segments) by taking into account of the boundary conditions of the whole beam. The solutions of = 0 (where denotes a determinant) give the “exact” natural frequencies of the constrained beam (carrying multiple spring-mass systems) and the substitution of each corresponding values of into the associated eigenfunctions for each attaching point will determine the corresponding mode shapes. Since no assumptions were made in the present approach (NAM), the natural frequencies and the corresponding mode shapes obtained are the exact ones.
目錄

誌謝 ii
摘要 iii
ABSTRACT iv
目錄 v
表目錄 vii
圖目錄 viii
符號與縮寫 ix
1. 緒論 1
1.1 前言 1
1.2 研究方法 3
2. 理論推導 4
2.1 不均勻 Euler樑之運動方程式及特徵函數 4
2.2 不均勻樑在第v個集中元素的附著點之係數矩陣 7
2.3 不均勻 Euler 樑左端之係數矩陣 12
2.4 不均勻 Euler 樑右端之係數矩陣 13
2.5 不均勻Euler樑附帶彈簧─質量懸吊系統時的整體係數矩陣及頻率方程式 15
2.6 不均勻Euler樑在各種支撐情況下的係數矩陣 、 16
3. 數值分析結果與討論 19
3.1 不均勻Euler樑無附帶與有附帶彈簧─質量懸吊系統之驗證 19
3.2 不均勻Euler樑無附帶任意個彈簧─質量懸吊系統之分析 20
3.3 不均勻Euler樑附帶任意彈簧─質量懸吊系統之分析 27
3.3.1 不均勻Euler樑附帶一個彈簧─質量懸吊系統 27
3.3.2 不均勻Euler樑附帶三個彈簧─質量懸吊系統 32
3.3.3 不均勻Euler樑附帶五個彈簧─質量懸吊系統 37
4. 結論 42
參考文獻 43
附錄 46
參考文獻

[1]Laura, P. A. A., Maurizi, M. J., and Pombo, J. L., “A note on the dynamic analysis of an elastically restrained-free beam with a mass at the free end,” Journal of Sound and Vibration, Vol. 41, pp. 397-405, 1975.
[2]Laura, P. A. A., Maurizi, M. J., Pombo, J. L., Luisoni, L. E., and Gelos, R., “On the dynamic behavior of structural elements carrying elastically mounted concentrated masses,” Applied Acoustic, Vol. 10, pp. 121-145, 1977.
[3]Gurgoze, M., “A note on the vibrations of restrained beam and rods with point masses,” Journal of Sound and Vibration, Vol. 96, pp. 461-468, 1984.
[4]Laura, P. A. A., Filipich, C. P., and Cortinez, V. H., “Vibration of beams and plates carrying concentrated masses, “Journal of Sound and Vibration, Vol. 112, pp. 177-182, 1987.
[5]Wu, J. S. and Lin, T. L., “Free vibration analysis of a uniform cantilever beam with point masses by an analytical-and-numerical-combined method,” Journal of Sound and Vibration, Vol. 136, pp. 201-213, 1990.
[6]Hamdan, M. N. and Jubran,B. A., “Free and forced vibrations of a restrained uniform beam carrying an intermediate lumped mass and a rotary inertia,” Journal of Sound and Vibration, Vol. 150, pp. 203-216, 1991.
[7]Rossi, R. E. Laura, P. A. A., Avalos, D. R., and Larrondo, H., “Free Vibration of Timoshenko Beams Carrying Elastically Mounted,” Journal of Sound and Vibration, Vol. 165, pp. 209-223, 1993.
[8]Gurgoze, M., “On the alternative formulations of the frequency equations of a Bernoulli-Euler beam to which several spring-mass systems are attached inspan,” Journal of Sound and Vibration, Vol. 217, pp. 585-595, 1998.
[9]Wu, J. S. and Chou, H. M., “Free vibration analysis of a cantilever beam carrying any number of elastically mounted point masses with the analytical-and-numerical-combined method,” Journal of Sound and Vibration, Vol. 213, pp. 317-332, 1998.
[10]Wu, J. S. and Chou, H. M., “A new approach for determining the natural frequencies and mode shapes of a uniform beam carrying any number of sprung masses,” Journal of Sound and Vibration, Vol. 220, pp. 451-468, 1999.
[11]Wu, J. S., Chen, D. W., and Chou, H. M., “On the eigenvalues of a uniform cantilever beam carrying any number of spring-damper-mass system,” International Journal for Numerical Methods in Engineering, Vol. 45, pp. 1277-1295, 1999.
[12]Wu, J. S. and Chen, D. W., “Free vibration analysis of a Timoshenko beam carrying Multiple spring-mass systems by using the numerical assembly technique,” International Journal for Numerical Methods in Engineering , Vol. 50, pp. 1039-1058, 2001.
[13]Housner, G. W. and Keightley, W. O., “Vibrations of linearly tapered cantilever beams,” Journal of Engineering Mechnics Division, Proceedings of the ASCE, Vol. 88, EM2, pp. 95-123, 1962.
[14]Heidebrecht, A. C., “Vibrations of non-uniform simply-supported beams,” Journal of Engineering Mechnics Division, Proceedings of the ASCE, 93, EM2, pp. 1-15, 1967.
[15]Gupta, A. K., “Vibration of tapered beams,” Journal of Structural Engineering, Vol. 111, pp. 19-15, 1985.
[16]Abrate, S., “Vibration of non-uniform rods and beams,” Journal of Sound and Vibration, Vol. 185, pp. 703-716, 1995.
[17]Naguleswaran, S., “Comments on Vibration of non-uniform rods and beams,” Journal of Sound and Vibration, Vol. 195, pp. 331-337, 1996.
[18]De Rosa, M. A. and Auciello, N. M., “Free vibrations of tapered beams with flexible ends,” Computers and Structures, Vol. 60, pp. 197-202, 1996.
[19]Wu, J. S. and Hsieh, M., “Free vibration analysis of a non-uniform beam with multiple point masses,” Structural Engineering and Mechanics, Vol. 9, pp. 449-467, 2000.
[20]Gorman, Daniel I., Free vibration analysis of beams and shafts, by John Wiley & Sons, Inc, 1975.
[21]Karman, Theodore V., and A.Biot, Maurice, Mathematical methods in Engineering, New York: McGraw-Hill, 1940.
[22]Faires, J. D. and Burden, R. L., Numerical Methods, PWS Publishing Company, Boston, USA, 1993.
[23]Laura, P. A. A., Susemihl, E. A., Pombo, L. E., Luisoni, L. E., and Gelos, R., “On the dynamic behavior of structural elements carrying elastically mounted,” concentrated masses, Applied Acoustics, Vol. 10, pp. 121-145, 1977.
[24]Cranch, E. T. and Alfred, A. A., “Bending vibration of variablesection beams,” Journal of Applied Mechanics, ASME, March 1956.
QRCODE
 
 
 
 
 
                                                                                                                                                                                                                                                                                                                                                                                                               
第一頁 上一頁 下一頁 最後一頁 top