進階搜尋


 
系統識別號 U0026-0812200910415963
論文名稱(中文) 小波有限元素法在旋轉葉片上的振動分析
論文名稱(英文) The Vibration Analyses of Rotary Blade by Using The Wavelets Finite Element Method
校院名稱 成功大學
系所名稱(中) 機械工程學系碩博士班
系所名稱(英) Department of Mechanical Engineering
學年度 91
學期 2
出版年 92
研究生(中文) 王中民
研究生(英文) Chung-Mean Wang
學號 n1690147
學位類別 碩士
語文別 中文
論文頁數 64頁
口試委員 指導教授-陳聯文
口試委員-賴新一
口試委員-許來興
中文關鍵字 小波有限元素法  小波函數 
英文關鍵字 wavelets function  wavelets finite element method 
學科別分類
中文摘要 旋轉機械目前已成為機械技術領域中相當重要的一環,其中的設計問題又以旋轉葉片的振動分析最為關鍵。在傳統上,為了求得旋轉葉片的自然振動頻率,以有限元素法(finite element method)來作分析是常見的一種方式。
在有限元素法中,為求得更精確的解,可藉由提高單位元素的數目或者增加節點上的自由度來達成,但這會耗費許多計算上的時間。因此本文利用小波函數(wavelets)中的”尺度函數”(scalets),作為小波有限元素法中的內插形狀函數,小波係數作為單位元素自由度,再使用一空間轉換矩陣將小波空間中的自由度轉為實際的節點位移函數,並測試其在不同條件下的收斂性。
本文選擇Daubechies小波函數作為內插形狀函數,因其具有正交性、有限承載與良好的頻域及時域局部定位解析特性。由分析結果可以得知,小波有限元素法的確具有相當的可靠性及優異的收斂性,能減少計算時所需之單位元素數目,進而提高計算上的效率。
英文摘要 The rotary machines have been the important part of the mechanical technology fields. Among the design problems, the vibration analyses of the rotary blades are the key points. In order to get the natural frequencies of vibration, we usually use the finite element methods.
In the finite element method, we obtain the better solutions by increasing the element numbers, but this waste much time in computation. Therefore, we employ the “scalets” of the “wavelets” as the new interpolation functions, and the “wavelet coefficients” as the degrees of freedom. We must construct space transform matrix to transform the wavelet coefficients to nodal displacement functions. After all, their convergence in different conditions is tested.
Daubechies wavelets possess elegant properties of orthonormal, compact support and time-frequency localization. As the results, the wavelets finite element method has better convergence with less element numbers and improves the efficiency in calculation.
論文目次 摘要 I
Abstract II
誌謝 III
目錄 IV
表目錄 VI
圖目錄 VIII
符號說明 Ⅹ

第一章 緒論 1
1-1 前言 1
1-2 文獻回顧 2
1-3 論文大綱 4

第二章 小波理論 6
2-1 多層次解析之基本概念 6
2-2 Daubechies小波函數及尺度函數之計算 11
2-3 Daubechies小波之尺度函數微分值計算 14
2-4 尺度函數動量值 15
2-5 Daubechies小波之聯結係數 17

第三章 小波有限元素法 28
3-1 旋轉葉片的有限元素法分析 28
3-2旋轉葉片的小波有限元素法分析 33

第四章 結果與討論 42
4-1薄葉片的自然振動頻率分析結果 42
4-2結論 44

第五章 綜合結論與未來展望 57
5-1綜合結論 57
5-2未來展望 58

參考文獻 59

自述 64
參考文獻 1.Amara, G., ”An Introduction to Wavelets”, IEEE Computational Science and Engineering, Vol. 2, pp.1-18, summer (1995).

2.Morlet, J. and Grossmann, A., “Decomposition of Hardy Functions Into Square Integrable Wavelets of Constant Shape”, SIAM J. Math. Anal., Vol. 15, pp.723-736 (1984).

3.Meyer. Y., “Principle d’incertitude, bases Hilbertiennes et algèbres d’opèrateurs”, Sèminare Bourbaki , No. 662, (1985).

4.Battle, G., “ A Block Spin Construction of Ondelettes, Part 1: Lemarie Functions “, Commun. Math. Phys., Vol. 110, pp.601-615 (1987).

5.Mallat, S., “Multiresolution Approximations and Wavelet Orthonormal Bases of L2(R)”, Trans. of Amer. Math. Soc. Vol.315, pp69-87 (1989).

6.Daubechies, I., “Orthonormal Bases of Compactly Supported Wavelets”, Commun. On Pure and Applied Math., Vol. 41, pp.909-996 (1988).

7.C.K. Chui and J.Z. Wang, ‘‘A Cardinal Spline Approach to Wavelets,’’ Proc. Amer. Math. Soc., Vol. 113, pp. 785-793 (1991).

8.Jaffard S., ‘‘Wavelet Methods for Fast Resolution of Elliptic Problems,’’ SIAM J. Numer. Anal. , Vol.29 No.4, pp. 965-986 (1992).

9.Bacry, E., Mallat, S. and Papanicolaou, G. ‘‘A Wavelets Based Space-time Numerical Method for Partial Differential Equations,’’ Mathematical Modeling and Numerical Analysis, Vol. 26, pp. 793-834 (1992).

10.J. C. Xu and W. C. Shann, ‘‘Wavelet-Galerkin Methods for Two-Point Boundary Value Problems,’’ Numer. Math., Vol. 63, pp. 123-144 (1992).

11.Qian, S. and Weiss, J. ‘‘Wavelets and the Numerical Solution of Boundary Value Problems,’’ Appl. Math. Lett. , Vol. 6, pp. 47-52 (1993).

12.M. Q. Chen, C. Hwang and Y. P. Shih, ‘‘A Wavelet-Galerkin Method for Solving population balance equations,’’ Computers & Chem. Engineering. (1994)

13.M. Q. Chen, C. Hwang and Y. P. Shih, ‘‘A Wavelet-Galerkin Method for Solving Stefan Problems,’’ J. Chinese Inst. Chem. Engrs, Vol. 26, No. 2, pp. 103-117 (1995).

14.M. Q. Chen, C. Hwang and Y. P. Shih, ‘‘Identification of A Linear Time-Varying System by A Wavelet-Galerkin Method,’’ Proc. of NSC, ROC-Part A : Physical Science and Engineering (1995).

15.H. L. Resnikoff, ‘‘Compactly Supported Wavelets and The Solution of Partial Differential Equations,’’ Tech. Report AD890926, Aware, Inc., Cambridge, USA., Vol. 26, pp. 1-9 (1989).

16.S. Jaffard and Ph. Laurecot, ‘‘Orthonormal Wavelets, Analysis of Operators, and Applications to Numerical Analysis,’’ In C. K. Chui (ed), Wavelets-A Tutorial in Theory and Applications, pp. 543-601 (1992).

17.C. Zhiqian and E. Weinan, ‘‘Hierarchical Method for Elliptic Problems Using Wavelet,’’ Communication in Applied Numerical Methods, Vol. 8, pp. 819-825 (1992).

18.W. Dahmen and C. A. Micchelli, 1993,‘‘Using the Refinement Equation for Evaluating Integrals of Wavelets,’’ SIAM J. Math. Anal. , Vol. 30, No. 2, pp. 507-537 (1993).

19.G. Beylkin, ‘‘On the Representation of Operators in Bases of Compactly Supported Wavelets,’’ SIAM J. Math. Anal. , Vol. 29, No. 6, pp. 1716-1740 (1992).

20.A. Lotto, H. L. Resnikoff and E. Tenenbaum, June ‘‘The Evaluation of Connection Coefficients of Compactly Supported Wavelets,’’ in Y. Maday(ed), Proc. of the French-USA Workshop on Wavelets and Turbulence, Princeton University, New York, Springer-Verlag (1991).

21.Amaratunga, K., Williams, J. R., Qian, S. and J. Weiss, ‘‘Wavelet-Galerkin Solutions for One-Dimensional Partial Differnetial Equations,’’ Int. J. for Num. Methods in Engineering, Vol. 37, pp. 2703-2716 (1994).

22.Ko, J., Kurdila, A. J. and Pilant, M. S.‘‘A Class of Finite Element Methods Based Orthonormal, Compactly Supported Wavelets,’’ Computational Mechanics, Vol. 16, pp. 235-244 (1995).

23.林政源,2003,”小波有限元素法在結構振動之應用”,國立成功大學機械工程學系碩士論文。

24.Carnegie, W., “Vibrations of Rotating Cantilever Blading: Theoretical Approaches to The Frequency Problem Based on Energy Methods,” Journal of Mechanical Engineering Sciences, Vol. 1, No.3, pp.235-240 (1959).

25.Carnegie, W., Dawson, B. and Thomas, J., “Vibration Characteristics of Cantilever Blading,” Proc. Instn. Mech. Engrs., Vol. 180, pp.71-89 (1965).

26.Carnegie, W., Stirling, C., and Fleming, J., “Vibration Characteristics of Turbine Blading under Rotation Results of An Initial Investigation and Details of High Speed Test Installation,” Proceedings of the Institution of Mechanical Engineers, Vol. 180, No.31, pp.1-9 (1966).

27.Carnegie, W. and Dawson, B., “Vibration Characteristics of Pre-Twisted Blades of Asymmetrical Aerofoil Cross-Section,” The Aeronautical Quarterly, August, pp. 257-273 (1971).

28.Carnegie, W., and Thomas, J., “The Coupled Bending-Bending Vibration of Pre-twisted Tapered Blading,” J. of Engr. for Industry ASME, February, pp. 255-266 (1972).

29.Barsoum, R. S., “Finite Element Method Applied to the Problem of Stability of a Non-conservative System,” International Journal for Numerical Methods in Engineering, Vol. 3, pp. 63-87 (1971).

30.Thomas, D. L., Wilson, J. M., and Wilson, R. R., “Timoshenko Beam Finite Elements,” Journal of Sound and Vibration, Vol. 31, pp. 315-330 (1973).

31.Stafford, R. O., and Giurgiutiu, V., “Semi-Analysis Methods for Rotating Timoshenko Beams,” International Journal of Mechanical Sciences, Vol. 17, pp. 719-727 (1975).

32.Abbas, B. A. H., “Dynamic Analysis of Thick Rotating Blades with Flexible Roots,” Aeronautical Journal, Vol. 89, pp.10-16 (1985).

33.Lien-Wen Chen and J. L. Chen, “Nonconservative Stability Analysis of a Cracked Thick Rotating Blade”, Computers and Structures, Vol.35, no.6, pp653-660 (1990).

34.Chung-Yi Lin and Lien-Wen Chen, “Dynamic stability of rotating composite beams with a viscoelastic core”, Composite Structures, Vol 58,pp185-194 (2002).

35.Dokumaci, E., ”Pre-twisted beam elements based on approximation of displacements in fixed directions”, Journal of Sound and vibration, Vol.52, no.2, pp277-282 (1977).

36.Thomas, J. and Carnegie, W. “The effects of shear deformation and rotary inertia on the lateral frequencies of cantilever beams in bending”, Journal of Engineering for industry ASME, February: 267-278 (1972).

37.Swaminathan, M. and Rao. J. S., “Vibrations of rotating pretwisted and tapered blades”, Mechanism and Machine Theory, Vol.12, no.4, pp331-337 (1977).

38.Ansari, Ka., “Nonlinear vibrations of a rotating pretwisted blade”, Computers and Structures, Vol.5, no.2, pp101-118 (1975).

39.Yang, SM. Tsao, SM., “Dynamics of a pretwisted blade under nonconstant rotating speed” Computers and Structures, Vol.62, no.4, pp6431-651 (1997).

40.黃國良,1999,”以小波表達城市幾何表面之新方法”,國立成功大學測量工程學系碩士論文。
41.單維彰,1998,”凌波初步”,全華圖書公司。

42.Strang, G. “Wavelets and Dilation Equation : A Brief Introduction” SIAM Review , Vol.31, pp614-627 (1989).

43.Rao, S. S., “Mechanical Vibrations”, Addison-Wesley, New York (1995).

44.陳炯錄,2001,”迴轉葉片之隨機振動與可靠度分析”,國立成功大學機械工程學系博士論文。
論文全文使用權限
  • 同意授權校內瀏覽/列印電子全文服務,於2003-07-30起公開。
  • 同意授權校外瀏覽/列印電子全文服務,於2003-07-30起公開。


  • 如您有疑問,請聯絡圖書館
    聯絡電話:(06)2757575#65773
    聯絡E-mail:etds@email.ncku.edu.tw