Title:
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Torsional asymmetry in suspension bridge systems (English) |
Author:
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Malík, Josef |
Language:
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English |
Journal:
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Applications of Mathematics |
ISSN:
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0862-7940 (print) |
ISSN:
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1572-9109 (online) |
Volume:
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60 |
Issue:
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6 |
Year:
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2015 |
Pages:
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677-701 |
Summary lang:
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English |
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Category:
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math |
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Summary:
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In this paper a dynamic linear model of suspension bridge center spans is formulated and three different ways of fixing the main cables are studied. The model describes vertical and torsional oscillations of the deck under the action of lateral wind. The mutual interactions of main cables, center span, and hangers are analyzed. Three variational evolutions are analyzed. The variational equations correspond to the way how the main cables are fixed. The existence, uniqueness, and continuous dependence on data are proved. (English) |
Keyword:
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suspension bridge |
Keyword:
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Hamilton principle |
Keyword:
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vertical oscillation |
Keyword:
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torsional oscillation |
Keyword:
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existence |
Keyword:
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uniqueness |
Keyword:
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continuous dependence on data |
MSC:
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35L57 |
MSC:
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35Q74 |
idZBL:
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Zbl 06537668 |
idMR:
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MR3436568 |
DOI:
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10.1007/s10492-015-0117-3 |
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Date available:
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2015-11-17T20:35:21Z |
Last updated:
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2020-07-02 |
Stable URL:
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http://hdl.handle.net/10338.dmlcz/144453 |
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Reference:
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[1] Ahmed, N. U., Harbi, H.: Mathematical analysis of dynamic models of suspension bridges.SIAM J. Appl. Math. 58 (1998), 853-874. Zbl 0912.93048, MR 1616611, 10.1137/S0036139996308698 |
Reference:
|
[2] An, Y.: Nonlinear perturbations of a coupled system of steady state suspension bridge equations.Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 51 (2002), 1285-1292. Zbl 1165.74323, MR 1926630, 10.1016/S0362-546X(01)00899-9 |
Reference:
|
[3] An, Y., Zhong, C.: Periodic solutions of a nonlinear suspension bridge equation with damping and nonconstant load.J. Math. Anal. Appl. 279 (2003), 569-579. Zbl 1029.35022, MR 1974046, 10.1016/S0022-247X(03)00035-0 |
Reference:
|
[4] Berkovits, J., Drábek, P., Leinfelder, H., Mustonen, V., Tajčová, G.: Time-periodic oscillations in suspension bridges: existence of unique solutions.Nonlinear Anal., Real World Appl. 1 (2000), 345-362. Zbl 0989.74031, MR 1791531 |
Reference:
|
[5] Choi, Y. S., Jen, K. C., McKenna, P. J.: The structure of the solution set for periodic oscillations in a suspension bridge model.IMA J. Appl. Math. 47 (1991), 283-306. Zbl 0756.73041, MR 1141492, 10.1093/imamat/47.3.283 |
Reference:
|
[6] Ding, Z.: Multiple periodic oscillations in a nonlinear suspension bridge system.J. Math. Anal. Appl. 269 (2002), 726-746. Zbl 1003.35089, MR 1907140, 10.1016/S0022-247X(02)00051-3 |
Reference:
|
[7] Ding, Z.: Nonlinear periodic oscillations in a suspension bridge system under periodic external aerodynamic forces.Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 49 (2002), 1079-1097. Zbl 1029.35023, MR 1942667, 10.1016/S0362-546X(01)00726-X |
Reference:
|
[8] Drábek, P., Leinfelder, H., Tajčová, G.: Coupled string-beam equations as a model of suspension bridges.Appl. Math., Praha 44 (1999), 97-142. Zbl 1059.74522, MR 1667633, 10.1023/A:1022257304738 |
Reference:
|
[9] Edwards, R. E.: Functional Analysis. Theory and Applications.Holt Rinehart and Winston New York (1965). Zbl 0182.16101, MR 0221256 |
Reference:
|
[10] Fonda, A., Schneider, Z., Zanolin, F.: Periodic oscillations for a nonlinear suspension bridge model.J. Comput. Appl. Math. 52 (1994), 113-140. Zbl 0810.73030, MR 1310126, 10.1016/0377-0427(94)90352-2 |
Reference:
|
[11] Gajewski, H., Gröger, K., Zacharias, K.: Nichtlineare Operatorgleichungen und Operatordifferentialgleichungen.German Mathematische Lehrbücher und Monographien. II. Abteilung. Band 38 Akademie-Verlag, Berlin (1974). MR 0636412 |
Reference:
|
[12] Glover, J., Lazer, A. C., McKenna, P. J.: Existence and stability of large scale nonlinear oscillations in suspension bridges.Z. Angew. Math. Phys. 40 (1989), 172-200. Zbl 0677.73046, MR 0990626, 10.1007/BF00944997 |
Reference:
|
[13] Holubová, G., Matas, A.: Initial-boundary value problem for the nonlinear string-beam system.J. Math. Anal. Appl. 288 (2003), 784-802. Zbl 1037.35087, MR 2020197, 10.1016/j.jmaa.2003.09.028 |
Reference:
|
[14] Lazer, A. C., McKenna, P. J.: Large-amplitude periodic oscillations in suspension bridges: some new connections with nonlinear analysis.SIAM Rev. 32 (1990), 537-578. Zbl 0725.73057, MR 1084570, 10.1137/1032120 |
Reference:
|
[15] Malík, J.: Generalized nonlinear models of suspension bridges.J. Math. Anal. Appl. 324 (2006), 1288-1296. Zbl 1139.74026, MR 2266559, 10.1016/j.jmaa.2006.01.003 |
Reference:
|
[16] Malík, J.: Nonlinear models of suspension bridges.J. Math. Anal. Appl. 321 (2006), 828-850. Zbl 1139.74026, MR 2241158, 10.1016/j.jmaa.2005.08.080 |
Reference:
|
[17] Malík, J.: Sudden lateral asymmetry and torsional oscillations in the original Tacoma suspension bridge.J. Sound Vib. 332 (2013), 3772-3789. 10.1016/j.jsv.2013.02.011 |
Reference:
|
[18] McKenna, P. J.: Large torsional oscillations in suspension bridges revisited: fixing an old approximation.Am. Math. Mon. 106 (1999), 1-18. Zbl 1076.70509, MR 1674145, 10.2307/2589581 |
Reference:
|
[19] McKenna, P. J., Walter, W.: Nonlinear oscillations in a suspension bridge.Arch. Ration. Mech. Anal. 98 (1987), 167-177. Zbl 0676.35003, MR 0866720, 10.1007/BF00251232 |
Reference:
|
[20] Plaut, R. H.: Snap loads and torsional oscillations of the original Tacoma Narrows Bridge.J. Sound Vib. 309 (2008), 613-636. 10.1016/j.jsv.2007.07.057 |
Reference:
|
[21] Plaut, R. H., Davis, F. M.: Sudden lateral asymmetry and torsional oscillations of section models of suspension bridges.J. Sound Vib. 307 (2007), 894-905. 10.1016/j.jsv.2007.07.036 |
Reference:
|
[22] Pugsley, A.: The Theory of Suspension Bridges.Edward Arnold, London (1968). |
Reference:
|
[23] Scanlan, R. H.: The action of flexible bridges under wind, I: Flutter theory.J. Sound Vib. 60 (1978), 187-199. Zbl 0384.73027, 10.1016/S0022-460X(78)80028-5 |
Reference:
|
[24] Scanlan, R. H.: The action of flexible bridges under wind, II: Buffeting theory.J. Sound Vib. 60 (1978), 201-211. Zbl 0384.73028, 10.1016/S0022-460X(78)80029-7 |
Reference:
|
[25] Simiu, E., Scanlan, R. H.: Wind Effects on Structures: Fundamentals and Applications to Design.Wiley, New York (1996). |
Reference:
|
[26] Tajčová, G.: Mathematical models of suspension bridges.Appl. Math., Praha 42 (1997), 451-480. Zbl 1042.74535, MR 1475052, 10.1023/A:1022255113612 |
Reference:
|
[27] Zeidler, E.: Nonlinear Functional Analysis and Its Applications. II/A: Linear Monotone Operators.Springer, New York (1990). Zbl 0684.47028, MR 1033497 |
Reference:
|
[28] : http://www.youtube.com/watch?v=3mclp9QmCGs.. |
Reference:
|
[29] : http://www.youtube.com/watch?v=j-zczJXSxnw.. |
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