簡易檢索 / 詳目顯示

回結果列表
研究生： 陳煜仁
Chen, Yu-Ren
論文名稱： 含黏彈層極正交三明治環板的振動與穩定性分析
Vibration and Dynamic Stability Analysis of Polar Orthotropic Annular Plates with a Viscoelastic Core Layer
指導教授： 陳聯文
Chen, Lien-Wen
學位類別： 博士
Doctor
系所名稱： 工學院 - 機械工程學系
Department of Mechanical Engineering
論文出版年： 2005
畢業學年度： 93
語文別： 中文
論文頁數： 89
中文關鍵詞： 極正交環板 、黏彈 、穩定性分析
外文關鍵詞： Viscoelastic, Dynamic Stability Analysis, Polar Orthotropic Annular Plates
相關次數： 點閱：72  下載：2 
分享至:
查詢本校圖書館目錄 查詢臺灣博碩士論文知識加值系統 勘誤回報

    • 摘 要

    　　本論文主要研究含黏彈層極正交三明治環板之自由振動、阻尼行為以及動態穩定特性。三明治環板系統的數學統制方程式是以離散層環狀有限元素法推導而成，而該有限元素包含有橫向剪力的效應可同時適用於薄板與厚板的問題。三明治環板系統中表層材料特性是彈性、極正交性和均質性。黏彈心層是等向性與線性阻尼，其材料特性是以複數的型式來加以描述，並且是不可壓縮的。靜止與旋轉三明治環板系統的自由振動、阻尼行為以及動態穩定性是本文所探討的重點。文中，旋轉和外加平面內負荷對環板系統造成的初始應力分佈是藉由靜態問題中之平衡位移進一步求解，接著系統的幾何剛性矩陣是由該應力分佈對應變能之貢獻項獲得。導出具複數係數的統制方程式後，由複數型式的特徵值問題即可解得系統之自然頻率、模態損失因子以及動態穩定與不穩定區域間的邊界。
    　　本文探討了數種參數，例如極正交表層與黏彈心層的材料性質和厚度，內外徑比，厚度比和旋轉速度對三明治環板系統之自然頻率、模態損失因子以及動態不穩定區域的影響。從數值分析的結果顯示，較厚的黏彈層並不會得到最佳的阻尼特性。系統的模態損失因子將隨著旋轉速度的增大而變小。此外，在三明治環板系統上極正交表層比模數的增加將使環板系統變得更為穩定。

    ABSTRACT

    　　Vibration, damping, and dynamic stability of polar orthotropic sandwich annular plates with a viscoelastic core layer are investigated. The governing equations of a polar orthotropic sandwich annular plate system are derived by a discrete layer annular finite element method. The transverse shear effects are included in the finite element, which conveniently handles the thick and thin plate problems. The material properties of the face layers are elastic, polar orthotropic and homogeneous. The material properties of isotropic, linear and incompressible viscoelastic materials in the damping layer are described by complex representations. The free vibration and dynamic stability of stationary and rotational sandwich annular plates are focused. In the mathematical modeling, initial stress distribution induced by rotational and external load effects are obtained from the solutions of static problems and are taken into account in the strain energy expression to calculate the geometry stiffness matrices. The governing equations with complex coefficients are developed, and natural frequencies, modal loss factors and boundaries between dynamic stability region and instability region are solved.
    　　The effects of many design parameters, including stiffness and thickness of the viscoelastic core layer and face layers, inner ratios and rotational speeds are discussed. Numerical results show that the thicker damping layer or the larger treatment size does not always provide better damping properties of annular plate systems. The modal loss factors of systems are decreased with increasing of rotational speeds. Moreover, increasing the modulus ratios of the face layers tends to stabilize annular plate systems.

    目 錄 摘要 i ABSTRACT ii 誌謝 iii 目錄 iv 表目錄 vii 圖目錄 viii 符號說明 xii 第一章 緒論 1 1-1 前言 1 1-2 文獻回顧 2 1-2-1 極正交圓/環板的自由振動 2 1-2-2 靜態挫曲 5 1-2-3 動態不穩定 6 1-2-4 含黏彈材料疊層板的動態穩定性 7 1-3 本文架構 9 第二章 極正交三明治靜止環板的自由振動分析 11 2-1 系統統制方程式的推導 11 2-1-1 基本離散層有限元素 11 2-1-2 應力-應變與應變-位移關係式 13 2-1-3 元素的質量與剛性矩陣 14 2-1-4 有限元素堆疊、邊界條件及求解 15 2-2 數值結果與討論 16 2-2-1 與文獻的比對和無因次化參數的引進 16 2-2-2 環板之外徑與厚度比的影響 17 2-2-3 表層極正交性的影響 17 2-2-4 黏彈層與表層厚度的影響 18 2-2-5 非對稱表層厚度與比模數的影響 18 2-3 結論 19 第三章 極正交三明治旋轉環板的軸對稱自由振動分析 29 3-1 系統統制方程式的推導 29 3-1-1 軸對稱離散層環狀有限元素 29 3-1-2 應力-應變與應變-位移關係式 30 3-1-3 元素的質量與剛性矩陣 31 3-1-4 有限元素組合、邊界條件與求解 33 3-1-5 元素節點平衡位移向量的求得 34 3-2 數值結果與討論 35 3-2-1 與文獻的比對和無因次化參數的引進 35 3-2-2 環板之外徑與厚度比的影響 36 3-2-3 黏彈層厚度的影響 36 3-2-4 表層厚度與比模數的影響 36 3-3 結論 37 第四章 極正交三明治靜止環板的動態穩定性分析 46 4-1 系統統制方程式的推導 46 4-1-1 運動方程式 46 4-1-2 外加負荷所致之元素節點平衡位移向量的求解 48 4-1-3 動態穩定性分析 49 4-2 結果與討論 51 4-2-1 無因次化參數的定義以及和文獻的比對 51 4-2-2 靜態與動態負荷的影響 51 4-2-3 內外徑比的效應 52 4-2-4 黏彈層厚度的影響 52 4-2-5 內外徑比和黏彈材料層厚度的不穩定區寬度 52 4-3 結論 52 第五章 極正交三明治旋轉環板的動態穩定性 62 5-1 數學推導 62 5-1-1 有限元素方程式推導 62 5-1-2 元素平衡位移向量的求解 63 5-1-3 動態穩定性分析 65 5-2 結果與討論 67 5-2-1 靜態負荷對無因次化頻率的影響 67 5-2-2 靜態與動態負荷對動態不穩定區的影響 67 5-2-3 旋轉速度對動態不穩定區的影響 68 5-3 結論 68 第六章 綜合結論與建議 75 6-1 綜合結論 75 6-2 未來研究方向與建議 76 參考文獻 77

    參考文獻

    [ 1] Rao, S.S., Mechanical Vibrations, Addison-Wesley, New York (1995).
    [ 2] Nashif, D., Jones, D.I.G., and Henderson, J.P., Vibration Damping, John Wiley & Sons, New York (1985).
    [ 3] Ugural, A.C., Mechanics of Materials, McGraw-Hill, New York (1991).
    [ 4] Bolotin, V.V., The Dynamic Stability of Elastic Systems, Holden-Day, San Francisco (1964).
    [ 5] Leissa, A.W., "Recent research in plate vibrations: classical theory," The Shock and Vibration Digest, Vol. 9, pp. 13-24 (1978).
    [ 6] Leissa, A.W., "Plate vibration research, 1976-1980: classical theory," The Shock and Vibration Digest, Vol. 13, pp. 11-22 (1981).
    [ 7] Leissa, A.W., "Recent studies in plate vibrations: 1981-1985, part I. classical theory," The Shock and Vibration Digest, Vol. 19, pp. 11-18 (1987).
    [ 8] Mindlin, R.D., "Influence of rotatory inertia and shear on flexural motions of isotropic, elastic plates," Journal of Applied Mechanics, Vol. 18, pp. 31-38 (1951).
    [ 9] Mindlin, R.D., and Deresiewicz, H., "Thickness-shear and flexural vibrations of a circular disk," Journal of Applied Physics, Vol. 25, pp. 1329-1332 (1954).
    [10] Rao, S.S., and Prasad, A.S., "Vibrations of annular plates including the effects of rotatory inertia and transverse shear deformation," Journal of Sound and Vibration, Vol. 42, pp.305-324 (1975).
    [11] Irie, T., Yamada, G., and Aomura, S., "Natural frequencies of Mindlin circular plates." Journal of Applied Mechanics, Vol. 47, pp.652-655 (1980).
    [12] Irie, T., Yamada, G., and Takagi, K., "Natural frequencies of thick annular plates." Journal of Applied Mechanics, Vol. 49, pp.633-638 (1982).
    [13] Doong, J.L., Nonlinear Analysis of Thick Plates, Ph.D. thesis, National Cheng Kung University, Taiwan (1983). (in Mandarin)
    [14] Hwang, J.R., Vibration and Stability of Thick Circular Plates, Ph.D. Thesis, National Cheng Kung University, Taiwan (1988). (in Mandarin)
    [15] Prathap, G., and Varadan, T. K.,”Axisymmetric Vibrations of Polar Orthotropic Circular Plates,” AIAA Journal, Vol. 14, NO. 11, pp. 1639-1640 (1976).

    [16] Lekhnitskii, S. G., Anisotropic Plates, Gordon and Breach Science Publisher, New York (1968).
    [17] Minkarah, I. A., and Hoppmann Ⅱ, W. H., “Flexural Vibration of Cylindrically Aeolortopic Circular Plate,” The journal of the Acoustical Society of America, Vol. 36, No. 3, pp. 470-475 (1964).
    [18] Ramaiah, G.. K., and Vijayakumar, K., “Natural Frequencies of Polar Orthotropic Annular Plates,” Journal of Sound and Vibration, Vol. 26, No.4, pp 303-310 (1973).
    [19] Greenberg, J. B., and Stavsky, Y., “Flexural Vibration of Certain Full and Annular Composite Orthotropic Plates,” Journal of the Acoustical Society of America, Vol. 66, No. 2, pp. 501-508 (1979).
    [20] Ginesu, F., Picasso, B. and Priolo, P., “Vibration Analysis of Polar Orthotropic Annular Discs,” Journal of Sound and Vibration, Vol. 65, No. 1, 1979, pp. 97-105.
    [21] Naria, Y., “Natural Frequencies of Completely Free Annular and Circular Plates Having Polar Orthotropy.” Journal of Sound and Vibration, Vol. 92, No.1, pp. 33-38 (1984).
    [22] Gorman, D. C., “Vibration and Stability Analysis of Polar Orthotropic Uniform Discs Subjected to Peripheral Hydrostatic Loading,” Journal of Sound and Vibration, Vol. 89, No. 4, pp. 477-486 (1983).
    [23] Chen, L.W., and Doong, J.L., "Vibrations of an initially stressed transversely isotropic circular thick plates." International Journal of Mechanical Science, Vol. 26, pp. 252-263 (1984).
    [24] Doong, J.L., and Chen, L.W., "Axisymmetric vibration of an initially stressed bimodulus thick circular plates." Journal of Sound and Vibration, Vol. 94, pp.461-468 (1984).
    [25] Chen, L.W., and Hwang, J.R., "Vibrations of initially stressed thick circular and annular plates based on a high-order plate theory," Journal of Sound and Vibration, Vol. 122, pp. 79-95 (1988).
    [26] Chen, L.W., and Juang, D.P., "Axisymmetric vibration of bimodulus thick circular and annular plates." Computers and Structures, Vol. 25, pp. 759-764 (1987).
    [27] Chen, L.W., and Hwang, J.R., "Finite element analysis of thick annular plates under internal forces." Computers and Structures, Vol. 32, pp. 63-68 (1989).

    [28] Chen, L.W., and Chen, C.C., "Asymmetric vibration and dynamic stability of bimodulus thick annular plates." Computers and Structures, Vol. 31, pp. 1013-1022 (1989).
    [29] Chen, L.W., and Doong, J.L., "Large-amplitude vibration of an initially stressed thick circular plate." American Institute of Aeronautics and Astronautics Journal, Vol. 9, pp. 1317-1324 (1983).
    [30] Lamb, H, and Southwell, R.V., "The vibrations of a spinning disk." Proceedings of the Royal Society of London, Vol. 99, pp. 272-280 (1921).
    [31] Southwell, R.V., "On the free transverse vibration of a uniform circular disk clamped at its center; and on the effects of rotation," Proceedings of the Royal Society of London, Vol. 101, pp. 133-153 (1922).
    [32] Eversman, W., and Dodson, R.O., "Free vibration of a centrally clamped spinning circular disk." American Institute of Aeronautics and Astronautics Journal, Vol. 7, pp. 2010-2013 (1969).
    [33] Barasch, S., and Chen, Y., "On the vibration of a rotating disk." Journal of Applied Mechanics, Vol. 39, pp. 1143-1144 (1972).
    [34] Sinha, S.K., "Determination of natural frequencies of a thick spinning annular disk using a Rayleigh-Ritz's trial function," Journal of the Acoustical Society of America, Vol. 81, pp. 357-369 (1987).
    [35] Mignolet, M.P., Eick, C.D., and Harish, M.V., "Free vibration of flexible rotating disks," Journal of Sound and Vibration, Vol. 196, pp. 537-547 (1996).
    [36] Pardoen, G.C., "Deflection function for the symmetrical bending of circular plates." American Institute of Aeronautics and Astronautics Journal, Vol. 10, pp. 239-240 (1972).
    [37] Kirkhope, J., and Wilson, G.J., "Vibration of circular and annular plates using finite elements." International Journal for Numerical Methods in Engineering, Vol. 4, pp. 181-193 (1972).
    [38] Kirkhope, J., and Wilson, G.J., "Vibration and stress analysis of thin rotating discs using annular finite elements," Journal of Sound and Vibration, Vol. 44, pp.461-474 (1976).

    [39] Kennedy, W., and Gorman, D., "Vibration analysis of variable thickness discs subjected to centrifugal and thermal stresses." Journal of Sound and Vibration, Vol. 53, pp. 83-101 (1977).
    [40] Nigh, G.L., Olson, M.D., "Finite element analysis of rotating disks," Journal of Sound and Vibration, Vol. 77, pp. 61-78 (1981).
    [41] Liu, C.F., Lee, J.F., and Lee, Y.T., "Axisymmetric vibration analysis of rotating annular plates by a 3D finite element." International Journal of Solids and Structures, Vol. 37, pp. 5813-5827 (2000).
    [42] Shen, I.Y., "Vibration of Flexible Rotating Disks," The Shock and Vibration Digest, Vol. 32, pp. 267-272 (2000).
    [43] Bryan, G.H., "Buckling of plates." Proceedings of the London Mathematical Society, Vol. 22, pp. 54-67 (1891).
    [44] Yamaki, N., "Buckling of a thin annular plate under uniform compression." Journal of Applied Mechanics, Vol. 25, pp. 267-273 (1958).
    [45] Ku, A.B., "The elastic buckling of circular plates." International Journal of Mechanical Science, Vol. 20, pp.593-597 (1978).
    [46] Majumdar, S., "Buckling of a thin annular plate under uniform compression." American Institute of Aeronautics and Astronautics Journal, Vol. 9, pp. 1701-1707 (1971).
    [47] Woinowsky-Krieger, S., "Buckling stability of circular plates with cylindrical aelotropy," Ingenieur-Archiv, Vol. 26, pp.129-131 (1958)
    [48] Pandalai, K. V. A. and Patel S. A., "Buckling of orthotropic circular plates," Aeronautical society, Vol. 69, pp. 279-280 (1965)
    [49] Swamidas, A. S. J. and Kunukkasseril, V. X., " Buckling of orthotropic circular plates," AIAA, Vol. 11, pp. 1633-1636 (1973)
    [50] Doong, J.L., and Chen, L.W., "Buckling of a thick circular plate." Journal of the Chinese Society of Mechanical Engineers, Vol. 5, pp. 107-112 (1984).
    [51] Juang, D.P., and Chen, L.W., "Axisymmetric buckling of bimodulus thick circular plates." Computers and Structures, Vol. 25, pp. 175-182 (1987).
    [52] Chen, L.W., and Hwang, J.R., "Axisymmetric dynamic stability of polar orthotropic thick circular plates." Journal of Sound and Vibration, Vol. 125, pp. 555-563 (1988).

    [53] Bonder, V.A., "The stability of plates subjected to longitudinal periodic forces," Priklandnaia Matematika I Mekhanika, Vol. 2, pp. 87-104 (1938).
    [54] Tani, J., and Nakamura, T., "Dynamic stability of annular plates under periodic radial loads." Journal of the Acoustical Society of America; Vol. 64, pp. 827-831 (1978).
    [55] Tani, J., and Nakamura, T., "Parametric resonance of annular plates under pulsating uniform internal and external loads with different periods," Journal of Sound and Vibration, Vol. 60, pp. 289-297 (1978).
    [56] Tani, J., and Nakamura, T., "Dynamic stability of annular plates under pulsating torsion." Journal of Applied Mechanics, Vol. 47, pp. 595-600 (1980).
    [57] Tani, J., "Dynamic stability of orthotropic annular plates under pulsating torsion." Journal of the Acoustical Society of America, Vol. 69, pp. 1688-1694 (1981).
    [58] Tani, J., and Doki, H., "Dynamic stability of orthotropic annular plates under pulsating radial loads." Journal of the Acoustical Society of America, Vol. 72, pp. 845-850 (1982).
    [59] Chen, L.W., and Juang, D.P., "Axisymmetric dynamic stability of a bimodulus thick circular plate." Computers and Structures, Vol. 26, pp. 933-939 (1987).
    [60] Chen, L.W., Hwang, J.R., and Doong, J.L., "Asymmetric dynamic stability of thick annular plates based on a high-order plate theory," Journal of Sound and Vibration, Vol. 130, pp. 425-437 (1989).
    [61] Mead, D.J., "The effect of certain damping treatments on the responses of idealized aeroplane structures excited by noise." Air Force Materials Laboratory Report, AFML-TR-65-284, WPAFB (1965).
    [62] Kerwin, E.M., "Damping of flexural waves by a constrained viscoelastic layer," Journal of the Acoustical Society of America, Vol. 31, pp. 952-962 (1959).
    [63] Ross, D., Ungar, E.E., and Kerwin, E.M., "Damping of plate flexural vibrations by means of viscoelastic laminate." Structure Damping, Sec. 3, pp. 49-88 (1959).
    [64] DiTaranto, R.A., "Theory of vibratory bending for elastic and viscoelastic layered finite-length beams." Journal of Applied Mechanics, Vol. 32, pp. 881-886 (1965).
    [65] DiTaranto, R.A., "Composite damping of vibrating sandwich beams." Journal of Engineering for Industry, Vol. 89B, pp. 633-638 (1967).

    [66] Mead, D.J., and Markus, S., "The forced vibrations of a three-layer damped sandwich beam with arbitrary boundary conditions," Journal of Sound and Vibration, Vol. 10, pp. 163-175 (1969).
    [67] Mead, D.J., and Markus, S., "Loss factors and resonant frequencies of damped sandwich beams." Journal of Sound and Vibration, Vol. 12, pp. 99-112 (1970).
    [68] Lu, Y.P., and Douglas, B.E., "On the forced vibrations of three-layer damped sandwich beams." Journal of Sound and Vibration, Vol. 32, pp. 513-516 (1974).
    [69] Douglas, B.E., and Yang, J.C.S., "Transverse compressional damping in the vibratory response of elastic-viscoelastic-elastic beams." American Institute of Aeronautics and Astronautics Journal, Vol. 16, pp. 925-930 (1978).
    [70] Roy, P.K., and Ganesan, N.A., "Vibration and damping analysis of circular plates with constrained damping layer treatment." Computers and Structures, Vol. 49, pp. 269-274 (1993).
    [71] Yu, S.C., and Huang, S.C., "Vibration of a three-layered viscoelastic sandwich circular plate." International Journal of Mechanical Sciences, Vol. 43, pp. 2215-2236 (2001).
    [72] Kung, S.W., and Singh, R., "Vibration analysis of beams with multiple constrained layer damping patches," Journal of Sound and Vibration, Vol. 212, pp. 781-805 (1998).
    [73] Kung, S.W., and Singh, R., "Complex eigensolutions of rectangular plates with damping patches," Journal of Sound and Vibration, Vol. 216, pp. 1-28 (1998).
    [74] Kung, S.W., and Singh, R., "Development of approximate methods for the analysis of patch damping design concepts." Journal of Sound and Vibration, Vol. 219, pp. 785-812 (1999).
    [75] Stevens, K.K., "On the parametric excitation of a viscoelastic column." American Institute of Aeronautics and Astronautics Journal, Vol. 4, pp. 2111-2116 (1966).
    [76] Stevens, K.K., "Transverse vibration of a viscoelastic column with initial curvature under periodic axial load." Journal of Applied Mechanics, Vol. 36, pp. 814-818 (1969).
    [77] Stevens, K.K., and Evan-Iwanowski, R.M., "Parametric resonance of viscoelastic columns." International Journal of Solids and Structures, Vol. 5, pp. 755-765 (1969).

    [78] Dost, S., and Glockner, P.G., "On the dynamic stability of viscoelastic perfect columns." International Journal of Solids and Structures, Vol. 18, pp. 587-596 (1982).
    [79] Cederbaum, G., and Mond, M., "Stability properties of a viscoelastic column under a periodic force." Journal of Applied Mechanics, Vol. 59, pp. 16-19 (1992).
    [80] Cederbaum, G., and Mond, M., "On the dynamic stability of viscoelastic columns." Journal of Sound and Vibration, Vol. 222, pp. 329-330 (1999).
    [81] Fung, R.F., Huang, J.S., and Chen, W.H., "Dynamic stability of a viscoelastic beam subjected to harmonic and parametric excitations simultaneously," Journal of Sound and Vibration, Vol. 198, pp. 1-16 (1996).
    [82] Aboudi, J., Cederbaum, G., and Elishakoff, I., "Stability of viscoelastic plates by Lyapunov exponent," Journal of Sound and Vibration, Vol. 139, pp. 459-468 (1990).
    [83] Cederbaum, G., Aboudi, J., and Elishakoff, I., "Dynamic stability of viscoelastic composite plates via the Lyapunov exponents." International Journal of Solids and Structures, Vol. 28, pp. 317-327 (1991).
    [84] Touati, D., and Cederbaum, G., "Dynamic stability of nonlinear viscoelastic plates." International Journal of Solids and Structures, Vol. 31, pp. 2367-2376 (1994).
    [85] Ilyasov, M.H., and Aköz, A.Y., "The vibration and dynamic stability of viscoelastic plates." International Journal of Engineering Science, Vol. 38, pp. 695-714 (2000).
    [86] Lin, C.C., and Tseng, C.S., "Free vibration of polar orthotropic laminated circular and annular plates." Journal of Sound and Vibration; Vol. 209, pp. 797-810 (1998).
    [87] Cupial, P., and Niziol, J., "Vibration and damping analysis of a three-layered composite plate with a viscoelastic mid-layer." Journal of Sound and Vibration, Vol. 183, pp. 99-114 (1995).

    下載圖示 校內：立即公開
    校外：2005-07-15公開
    QR CODE