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研究生:周鴻泉
研究生(外文):chou hung chuan
論文名稱:Lazer-McKenna吊橋模型週期解路徑之數值探討
論文名稱(外文):The Numerical Investigation of Periodic Solution Path of Lazer-McKenna Suspension Bridge Model
指導教授:簡國清簡國清引用關係
指導教授(外文):K. C. Jen
學位類別:碩士
校院名稱:國立新竹師範學院
系所名稱:數理研究所
學門:數學及統計學門
學類:數學學類
論文種類:學術論文
論文出版年:2002
畢業學年度:90
語文別:中文
論文頁數:91
中文關鍵詞:打靶法Cran-Nicolson法隱函數定理虛擬弧長延拓法分歧圖多重週期解
外文關鍵詞:Shooting methodCrank-Nicolson methodImplicit function theoremPesudoarclength continuation methodBifurcation diagramMultiple periodic solution
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  • 被引用被引用:1
  • 點閱點閱:257
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  • 下載下載:20
  • 收藏至我的研究室書目清單書目收藏:0
本文主要在探討Lazer-McKenna吊橋模型的多重週期解。欲求並延拓非線性偏微分方程組之週期解是一種很困難的工作,本文提供一種演算法來求整個解路徑,並延拓隨著一個參數變動的非線性偏微分方程組之週期解,我們稱之為虛擬弧長延拓法(Pesudoarclength continuation method)。我們將虛擬弧長延拓法應用在Lazer-McKenna吊橋模型上,而虛擬弧長延拓法是基於打靶法、牛頓法、Crank-Nicolson法、猜測及解法(predictor-solver)及隱函數定理等數值方法,且我們將利用其來探討Lazer-McKenna吊橋模型週期解的解路徑。本文中,我們將藉由係數的改變、分歧圖的討論及週期解圖形的探討,並說明產生多重週期解的參數區間與初始條件的相互關係。
The main purpose of this paper is to investigate the multiple periodic solution of the Lezer-McKenna suspension bridge model.To obtain and continue the path of periodic solution of the systems of nonlinear partial differential equation is a more difficult task. An algorithm for continuation of the path of periodic solutions in partial differential equations dependent on a parameter is pre-sented in this article and is successfully applied to the Lezer-McKenna suspension bridge model. The pseudoarclength continuation method for the continuation of path of periodic solutions is based on the shooting method, Newton method, Crank-Nicolson method, predictor-solver method and implicit function theorem. We will use pseudoarclength continuation method to investigate the path of the Lazer-McKenna suspension bridge periodic solutions. In this paper, we discuss bifur-cation diagrams and graphs of periodic solution of our model dependent on several coefficients. We also discuss the relationship between the parameter interval of multi-ple periodic solutions and initial conditions of the model.
第一章 緒論
第二章 分歧理論與虛擬弧長延拓法
2.1 分歧問題
2.2 分歧理論
2.3 局部延拓法
2.3.1 預測法
2.3.2 解法
2.4 虛擬弧長延拓法
第三章 數值解法
3.1 u_xxxx項的離散
3.2 初始值問題解法
3.3 週期解之求法
3.4 虛擬弧長延拓法求解路徑
3.5 Lazer-McKenna吊橋模型週期解之主要演算法
第四章 數值實驗
4.1 演算法的測試
4.2 分歧圖的定性分析
4.3 係數改變的影響
4.4 多重週期解區間
4.5 多重週期解的立體圖
第五章 結論
參考文獻
[1]Aselone, P. M. and Moore, R. H., An Extension of the New-ton-Kantorovich Method for Sloving Nonlinear Equations with An Application to Elasticity. J. Math. Anal. 13, pp. 476-501, (1966).
[2]Bauer, L., Reiss, E. L., and Keller, H. B., Axisymmetric Bucking of Hollow Spheres and hemispheres, Comm. Pure Appl. Math., 23, pp. 529-568, (1970).
[3]Choi, Y. S., Jen, K. C., (簡國清) and McKenna, P. J., The Structure of the Solution Set for Periodic Oscillations in a Suspension Bridge Model, IMA J. Appl. Math., 47, pp. 283-306, (1991).
[4]Coron, J. M., Periodic Solutions of a Nonlinear Wave Equation with-out Asumptions of Monotonicity. Math. Ann., 262, pp.273-285, (1983).
[5]Crandall, M. G., An Introduction to Constructive Aspects of Bifurca-tion Theorem, edited by P. H. Rabinowtiz, Academic Press, pp. 1-35, (1977).
[6]J. Glover, A. C. Lazer, and P. J. McKenna, Existence and Stability of Large Scale Nonlinear Oscillations in Suspension Bridges, Journal of Applied Mathematics and Physics Vol. 40, (1989).
[7]Jen, K. C.(簡國清), The Stability and Convergence of a Crank-Nicolson Scheme for a Nonlinear Beam Vibration Equation, Chinese Journal of Mathematics, Vol 23, No. 2, pp. 97-121, (1995).
[8]Kawada, T., & Hirai, A. Additional Mass Method - A New Ap-proach to Suspension Bridge Rehabitation. Official Proceedings, 2nd Annual International Bridge Conference. Engineers of Society of Western Pennsylvania. (1985).
[9]Keller, H. B., in“ Recent Advances in Numerical Analysis ”, Ed. by C. de Boor and G. H. Golub, Academic Press, New York, p. 73, (1978).
[10]Keller, H. B., Lectures on Numerical Methods in Bifurcation Prob-lems, TATA Institute of Fundamental Research, Springer-Verlag, (1987)
[11]Keller, H. B., Numerical Solution of Bifurcation and Nonlinear Ei-genvalue Problems, Applications of Bifurcation Theory, Edited By Rabinowitz, P. H., Academic Press, pp. 359-384, (1977).
[12]Kubicek, M. and Marek, M., Computational Methods in Bifurcation Theory and Dissipative Structures, Springer-Verlag, New York, (1983).
[13]Lazer,A.C., & McKenna, P. J. Large Scale Oscillatory Behaviour in loaded asymmetric systems. Ann. Inst. Henri Poincar''e: Analyse nonlin''eaire 4(3), pp. 243-274, (1987).
[14]Lazer, A.C., & McKenna, P. J., A Symmetry Theorem and Applica-tions to Nonlinear Partial Differential Equations. J. Diff. Eq. 72, pp. 95-106, (1988).
[15]Lazer, A.C., & McKenna, P. J., Large Amplitude Periodic Oscilla-tions in Suspension Bridge: Some New Connections with Nonlinear Analysis. SIAM Review. 32, No.4, pp. 537-578, (1989).
[16]Matsuzaki, M. Experimental Study on Vortex Excited Oscillation of Suspension Bridge Towers. Trans. Jap. Soc. Civil Eng. 15, 172-174, (1985).
[17]McKenna P. J. and Walter W., Nonlinear Oscillations in a Suspen-sion Bridge. Archive for Rational Mechanics and Analysis. 98(2), 167-177, (1987).
[18]McKenna, P. J. and Walter W., On the Mulitiplicity of the Solution Set of Some Nonlinear Boundary Value Problems. Nonlinear Analy-sis 8, pp. 893-907, (1984).
[19]Michael G. Crandall and Paul H. Rabinowitz, Bifurcation from Sim-ple Eigenvalues, Journal of Functional Analysis 8, pp. 321-340, (1971)
[20]Michael G. Crandall and Paul H. Rabinowitz, Mathematical Theory of Bifurcation, Bifurcation Phenomena in Mathematical physics and Related Topics, edit by C. Bardos and D. Bessis, NATO Advanced Study Institute Series, (1979).
[21]Michael G. Crandall, An Introduction to Constructive Aspects of Bi-furcation and The Implicit Function Theorem, Application of Bifurca-tion Theorem, edited by P. H. Rabinowtz, Academic Press, New York, 1-35, (1977).
[22]Patil, S. P. Response of Infinite Railroad Track to Vibrating Mass. J. Eng. Mech. 114, 688-703, (1988).
[23]Q-Heung Choi and Tacksun Jung, Periodic Solution of the Lazer-McKenna Suspension Bridge Equation, to be submitted , (1989).
[24]Rheinboldt, W. C., Solution Fields of Nonlinear Equations and Con-tinuation Methods, SIAM J. Numer. Anal., 17, pp. 221-237, (1980).
[25]Scanlan, R. H. Airfoil and Bridge Deck Flutter Derivatives. Proc. Am. Soc. Civil Eng. Eng. Mech. Div. Em6, 1717-1737, (1971).
[26]Scanlan, R.H. Developments in Low-speed Aeroelasticity in the Civil Engineering Field. AIAA Journal 20, 839-844, (1982).
[27]Wacker, H. (ed), Continuation Methods, Academic Press, New York, (1978).
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