1 |
von Kármán T . Festigkeitsprobleme im maschinenbau. Encycl der Mathematischen Wissenschaften, Leipzig, 1910, 4: 348- 352
|
2 |
Berger M H . A new approach to the analysis of large deflections of plates. J Appl Mech, 1955, 22: 465- 472
doi: 10.1115/1.4011138
|
3 |
Berger M S . On von Kármán's equations and the buckling of a thin elastic plate, I: The clamped plate. Comm Pure Appl Math, 1967, 20: 687- 719
doi: 10.1002/cpa.3160200405
|
4 |
Ciarlet P G . A justification of the von Kármán equations. Arch Rat Mech Anal, 1980, 73: 349- 389
doi: 10.1007/BF00247674
|
5 |
Ferrero A , Gazzola F . A partially hinged rectangular plate as a model for suspension bridges. Disc Cont Dynam Syst A, 2015, 35: 5879- 5908
doi: 10.3934/dcds.2015.35.5879
|
6 |
Gazzola F , Wang Y . Modeling suspension bridges through the von Kármán quasilinear plate equations. Progress in Nonlinear Differential Equations and Their Applications, 2015, 86: 269- 297
|
7 |
Wang Y . An evolution von Kármán equation modeling suspension bridges. Nonlin Anal, 2018, 169: 59- 78
doi: 10.1016/j.na.2017.12.002
|
8 |
Rocard Y. Dynamic Instability: Automobiles, Aircraft, Suspension Bridges. London: Crosby Lockwood, 1957
|
9 |
Al-Gwaiz G , Benci V , Gazzola F . Bending and stretching energies in a rectangular plate modeling suspension bridges. Nonlinear Anal TMA, 2014, 186: 18- 34
|
10 |
Arioli G , Gazzola F . Torsional instabilty in suspension bridges: the Tacoma Narrows Bridge case. Comm Nonlin Sci Numer Simul, 2017, 42: 342- 357
doi: 10.1016/j.cnsns.2016.05.028
|
11 |
Tacoma Narrows Bridges collapse, http://www.youtube.com/watch?v=3mclp9QmCGs, 1940
|
12 |
Chueshov I, Lasiecka I. Von Kármán Evolution Equations, Well-posedness and Long-Time Dynamics. New York: Springer-Verlag, 2010
|
13 |
Ferreira V , Gazzola F , Moreira dos Santos E . Instability of modes in a partially hinged rectangular plate. J Diff Equa, 2016, 261: 6302- 6340
|
14 |
Chang K C. Methods in Nonlinear Analysis. Berlin: Springer, 2005
|