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December  2015, 35(12): 5879-5908. doi: 10.3934/dcds.2015.35.5879

A partially hinged rectangular plate as a model for suspension bridges

1. 

Dipartimento di Scienze e Innovazione Tecnologica, Università del Piemonte Orientale "Amedeo Avogadro", Viale Teresa Michel 11, 15121 Alessandria, Italy

2. 

Dipartimento di Matematica Politecnico di Milano, Piazza Leonardo da Vinci, 32, 20133 Milano

Received  July 2013 Published  May 2015

A plate model describing the statics and dynamics of a suspension bridge is suggested. A partially hinged plate subject to nonlinear restoring hangers is considered. The whole theory from linear problems, through nonlinear stationary equations, ending with the full hyperbolic evolution equation is studied. This paper aims to be the starting point for more refined models.
Citation: Alberto Ferrero, Filippo Gazzola. A partially hinged rectangular plate as a model for suspension bridges. Discrete & Continuous Dynamical Systems, 2015, 35 (12) : 5879-5908. doi: 10.3934/dcds.2015.35.5879
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show all references

References:
[1]

Academic Press, New York, 1975.  Google Scholar

[2]

Comm. Pure Appl. Math., 12 (1959), 623-727. doi: 10.1002/cpa.3160120405.  Google Scholar

[3]

CRC Press, Taylor & Francis Group, London, 2008. Google Scholar

[4]

Federal Works Agency, 1941. Google Scholar

[5]

Appl. Math. Modelling, 39 (2015), 901-912. doi: 10.1016/j.apm.2014.06.022.  Google Scholar

[6]

J. Diff. Eq., 251 (2011), 2696-2727. doi: 10.1016/j.jde.2011.05.036.  Google Scholar

[7]

Earthquake Engineering & Structural Dynamics, 23 (1994), 1351-1367. doi: 10.1002/eqe.4290231206.  Google Scholar

[8]

Math. Ann., 98 (1928), 205-247. doi: 10.1007/BF01451590.  Google Scholar

[9]

Phys. Rev. E, 79 (2009), 051110, 11pp. doi: 10.1103/PhysRevE.79.051110.  Google Scholar

[10]

Electron. J. Diff. Equ., (2013), 1-47,  Google Scholar

[11]

Lecture Notes in Mathematics, 1991, Springer-Verlag, Berlin, 2010. doi: 10.1007/978-3-642-12245-3.  Google Scholar

[12]

Nonlinear Analysis, 74 (2011), 6696-6711. doi: 10.1016/j.na.2011.06.049.  Google Scholar

[13]

Arch. Rat. Mech. Anal., 207 (2013), 717-752. doi: 10.1007/s00205-012-0569-5.  Google Scholar

[14]

PhD Dissertation, University of Cambridge, 2004. See also http://www.bridgeforum.org/dir/collapse/type/ for the update of the Bridge failure database. Google Scholar

[15]

ASCE Press, 2010. doi: 10.1061/9780784410189.  Google Scholar

[16]

J. Reine Angew. Math., 1850 (2009), 51-88. doi: 10.1515/crll.1850.40.51.  Google Scholar

[17]

Springer, 2013. doi: 10.1007/978-1-4419-1276-3.  Google Scholar

[18]

Science, 235 (1987), 1038-1040. doi: 10.1126/science.235.4792.1038.  Google Scholar

[19]

Ann. Inst. H. Poincaré Anal. non Lin., 4 (1987), 243-274.  Google Scholar

[20]

SIAM Rev., 32 (1990), 537-578. doi: 10.1137/1032120.  Google Scholar

[21]

Comptes Rendus Acad. Sci. Paris, 129 (1899), 535-539. Google Scholar

[22]

Fourth edition, Cambridge Univ. Press, 1927. Google Scholar

[23]

Second edition, Cambridge University Press, Cambridge, 1989. doi: 10.1017/CBO9780511525193.  Google Scholar

[24]

Mathematical Surveys and Monographs, 162, American Mathematical Society, 2010. doi: 10.1090/surv/162.  Google Scholar

[25]

Amer. Math. Monthly, 106 (1999), 1-18. doi: 10.2307/2589581.  Google Scholar

[26]

Amer. Math. Monthly, 108 (2001), 738-745. doi: 10.2307/2695617.  Google Scholar

[27]

Arch. Rat. Mech. Anal., 98 (1987), 167-177. doi: 10.1007/BF00251232.  Google Scholar

[28]

SIAM J. Appl. Math., 50 (1990), 703-715. doi: 10.1137/0150041.  Google Scholar

[29]

Springer-Verlag, Berlin, 1968 (first edition in 1925). doi: 10.1007/978-3-642-99170-7.  Google Scholar

[30]

Bulletin des Sciences de la Société Philomathique de Paris, (1823), 92-102. Google Scholar

[31]

J. Sound and Vibration, 307 (2007), 894-905. doi: 10.1016/j.jsv.2007.07.036.  Google Scholar

[32]

ASCE Press, 2001. doi: 10.1061/9780784405420.  Google Scholar

[33]

Marcel Dekker Inc., New York, 2001. doi: 10.1201/9780203908723.  Google Scholar

[34]

Tacoma Narrows Bridge Collapse, http://www.youtube.com/watch?v=3mclp9QmCGs,, 1940., ().   Google Scholar

[35]

Annali Mat. Pura Appl., 19 (1940), 107-124. doi: 10.1007/BF02410542.  Google Scholar

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