Skip to main content
Fachgebiete
Automobil + Motoren Bauwesen + Immobilien Business IT + Informatik Elektrotechnik + Elektronik Energie + Nachhaltigkeit Finance + Banking Management + Führung Marketing + Vertrieb Maschinenbau + Werkstoffe Versicherung + Risiko
DE
EN
Bücher
Zeitschriften
Themenseiten
Organisationspsychologie Projektmanagement Marketing Smart Manufacturing
Weitere Formate
Podcasts Webinare Technik Webinare Wirtschaft Kongresse Veranstaltungskalender Awards
Jetzt Einzelzugang starten
Zugang für Unternehmen
Referenzkunden
SLX-Digitalkonferenz: Zukunftswerkstatt 2024

Mehr Umsatz mit Top-Kontakten

Am 7. Mai erfahren Sie, wie Vertriebsteams Leadgenerierung, Leadnurturing und Leadstrategien effizient steuern können.
Erweiterte Suche
Anmelden
nach oben
Erschienen in:
Brief History of Suspension Bridges Kapitel lesen Erstes Kapitel lesen

2015 | OriginalPaper | Buchkapitel

2. One Dimensional Models

verfasst von : Filippo Gazzola

Erschienen in: Mathematical Models for Suspension Bridges

Verlag: Springer International Publishing

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

The first attempts to model suspension bridges were to view the roadway as a beam. Although this point of view rules out an important degree of freedom, the torsion, it appears to be a reasonable approximation since the width of the roadway is much smaller than its length. In this chapter we review classical modeling of beams and cables and of their interaction.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Jetzt informieren
Vorheriges Kapitel Brief History of Suspension Bridges
Nächstes Kapitel A Fish-Bone Beam Model
Literatur
1.
A.M. Abdel-Ghaffar, Suspension bridge vibration: continuum formulation. J. Eng. Mech. 108, 1215–1232 (1982)
4.
N.U. Ahmed, H. Harbi, Mathematical analysis of dynamic models of suspension bridges. SIAM J. Appl. Math. 58, 853–874 (1998)CrossRefMATHMathSciNet
7.
C.J. Amick, J.F. Toland, Homoclinic orbits in the dynamic phase-space analogy of an elastic strut. Eur. J. Appl. Math. 3, 97–114 (1992)CrossRefMATHMathSciNet
9.
O.H. Ammann, T. von Kármán, G.B. Woodruff, The Failure of the Tacoma Narrows Bridge (Federal Works Agency, Washington, DC, 1941)
27.
28.
J.M. Ball, Stability theory for an extensible beam. J. Differ. Equ. 14, 399–418 (1973)CrossRefMATH
32.
V. Benci, D. Fortunato, Existence of solitons in the nonlinear beam equation. J. Fixed Point Theory Appl. 11, 261–278 (2012)CrossRefMATHMathSciNet
35.
E. Berchio, A. Ferrero, F. Gazzola, P. Karageorgis, Qualitative behavior of global solutions to some nonlinear fourth order differential equations. J. Differ. Equ. 251, 2696–2727 (2011)CrossRefMATHMathSciNet
45.
J. Berkovits, P. Drábek, H. Leinfelder, V. Mustonen, G. Tajčová, Time-periodic oscillations in suspension bridges: existence of unique solutions. Nonlinear Anal. Real World Appl. 1, 345–362 (2000)CrossRefMATHMathSciNet
48.
M.A. Biot, T. von Kármán, Mathematical Methods in Engineering: An Introduction to the Mathematical Treatment of Engineering Problems, vol. XII (McGraw-Hill, New York, 1940)
50.
F. Bleich, C.B. McCullough, R. Rosecrans, G.S. Vincent, The Mathematical Theory of Vibration in Suspension Bridges (U.S. Dept. of Commerce, Bureau of Public Roads, Washington, DC, 1950)
51.
I. Bochicchio, C. Giorgi, E. Vuk, Long-term damped dynamics of the extensible suspension bridge. Int. J. Differ. Equ., 19 pp. (2010). Art. ID 383420
52.
I. Bochicchio, C. Giorgi, E. Vuk, On some nonlinear models for suspension bridges, in Proceedings of the Conference Evolution Equations and Materials with Memory, Rome, 12–14 July 2010, ed. by D. Andreucci, S. Carillo, M. Fabrizio, P. Loreti, D. Sforza (2011)
53.
I. Bochicchio, C. Giorgi, E. Vuk, Long-term dynamics of the coupled suspension bridge system. Math. Models Methods Appl. Sci. 22, 22 (2012)CrossRefMathSciNet
54.
I. Bochicchio, C. Giorgi, E. Vuk, Asymptotic dynamics of nonlinear coupled suspension bridge equations. J. Math. Anal. Appl. 402, 319–333 (2013)CrossRefMATHMathSciNet
55.
J. Bodgi, S. Erlicher, P. Argoul, Lateral vibration of footbridges under crowd-loading: continuous crowd modeling approach. Key Eng. Mater. 347, 685–690 (2007)CrossRef
56.
D. Bonheure, Multitransition kinks and pulses for fourth order equations with a bistable nonlinearity. Ann. Inst. H. Poincaré Anal. Non Linéaire 21, 319–340 (2004)CrossRefMATHMathSciNet
57.
D. Bonheure, L. Sanchez, Heteroclinic orbits for some classes of second and fourth order differential equations, in Handbook of Differential Equation, vol. III (Elsevier Science, Amsterdam, 2006), pp. 103–202
59.
B. Breuer, J. Hórak, P.J. McKenna, M. Plum, A computer-assisted existence and multiplicity proof for travelling waves in a nonlinearly supported beam. J. Differ. Equ. 224, 60–97 (2006)CrossRefMATH
63.
D. Bruno, V. Colotti, F. Greco, P. Lonetti, A parametric deformability analysis of long span bridge schemes under moving loads, in Second International Conference on Bridge Maintenance, Safety and Management, IABMAS04, Kyoto, 2004, pp. 735–737
67.
J.R. Cash, D. Hollevoet, F. Mazzia, A.M. Nagy, Algorithm 927: the MATLAB code bvptwp.m for the numerical solution of two point boundary value problems. ACM Trans. Math. Softw. 39(2) (2013). Article 15
68.
C.A. Castigliano, Nuova teoria intorno all’equilibrio dei sistemi elastici. Atti Acc. Sci. Torino Cl. Sci. Fis. Mat. Nat. 11, 127–286 (1875/1876)
69.
C.A. Castigliano, Théorie de l’équilibre des systèmes élastiques et ses applications (A.F. Negro, Torino, 1879)
73.
A.R. Champneys, P.J. McKenna, On solitary waves of a piecewise linear suspended beam model. Nonlinearity 10, 1763–1782 (1997)CrossRefMATHMathSciNet
75.
Y. Chen, P.J. McKenna, Traveling waves in a nonlinearly suspended beam: theoretical results and numerical observations. J. Differ. Equ. 136, 325–355 (1997)CrossRefMATHMathSciNet
78.
Q.H. Choi, T. Jung, P.J. McKenna, The study of a nonlinear suspension bridge equation by a variational reduction method. Appl. Anal. 50, 73–92 (1993)CrossRefMathSciNet
84.
M. Como, in Stabilità aerodinamica dei ponti di grande luce. Introduzione all’ingegneria strutturale, ed. by E. Giangreco (UTET, Torino, 2002)
85.
M. Como, S. Del Ferraro, A. Grimaldi, A parametric analysis of the flutter instability for long span suspension bridges. Wind Struct. 8, 1–12 (2005)CrossRef
87.
L. D’Ambrosio, J.P. Lessard, A. Pugliese, Blow-up profile for solutions of a fourth order nonlinear equation. Nonlinear Anal. T.M.A. (2015, to appear)
90.
K. Deckelnick, H.-Ch. Grunau, Boundary value problems for the one-dimensional Willmore equation. Calc. Var. 30, 293–314 (2007)CrossRefMATHMathSciNet
93.
94.
95.
Z. Ding, On nonlinear oscillations in a suspension bridge system. Trans. Am. Math. Soc. 354, 65–274 (2001)
97.
P. Drábek, P. Nečesal, Nonlinear scalar model of a suspension bridge: existence of multiple periodic solutions. Nonlinearity 16, 1165–1183 (2003)CrossRefMATHMathSciNet
98.
P. Drábek, G. Holubová, Bifurcation of periodic solutions in symmetric models of suspension bridges. Topol. Methods Nonlinear Anal. 14, 39–58 (1999)MATHMathSciNet
99.
P. Drábek, G. Holubová, A. Matas, P. Nečesal, Nonlinear models of suspension bridges: discussion of the results. Appl. Math. 48, 497–514 (2003)CrossRefMATHMathSciNet
100.
P. Drábek, H. Leinfelder, G. Tajčová, Coupled string-beam equations as a model of suspension bridges. Appl. Math. 44, 97–142 (1999)CrossRefMATHMathSciNet
102.
L. Euler, Methodus inveniendi lineas curvas maximi minimive proprietate gaudentes sive solutio problematis isoperimetrici latissimo sensu accepti (Marcum Michaelem Bousquet & Socios, Lausanne/Geneva, 1744)
110.
113.
A. Fonda, Z. Schneider, F. Zanolin, Periodic oscillations for a nonlinear suspension bridge model. J. Comput. Appl. Math. 52, 113–140 (1994)CrossRefMATHMathSciNet
119.
B.G. Galerkin, Sterzhni i plastinki: reydy v nekotorykh voprosakh uprugogo ravnovesiya sterzhney i plastinok. Vestnik Inzhenerov 1(19), 897–908 (1915)
121.
F. Gazzola, Nonlinearity in oscillating bridges. Electron. J. Differ. Equ. 211, 1–47 (2013)MathSciNet
122.
123.
F. Gazzola, H.-Ch. Grunau, G. Sweers, Polyharmonic Boundary Value Problems. Lecture Notes in Mathematics, vol. 1991 (Springer, Berlin, 2010)
124.
F. Gazzola, M. Jleli, B. Samet, On the Melan equation for suspension bridges. J. Fixed Point Theory Appl. 16 (2014)
125.
F. Gazzola, P. Karageorgis, Refined blow-up results for nonlinear fourth order differential equations. Commun. Pure Appl. Anal. 12, 677–693 (2015)MathSciNet
126.
F. Gazzola, R. Pavani, Blow up oscillating solutions to some nonlinear fourth order differential equations. Nonlinear Anal. T.M.A. 74, 6696–6711 (2011)
128.
F. Gazzola, R. Pavani, Wide oscillations finite time blow up for solutions to nonlinear fourth order differential equations. Arch. Ration. Mech. Anal. 207, 717–752 (2013)CrossRefMATHMathSciNet
129.
F. Gazzola, R. Pavani, The impact of nonlinear restoring forces acting on hinged elastic beams. Bull. Belgian Math. Soc. (2015)
133.
D. Gilbert, On the mathematical theory of suspension bridges, with tables for facilitating their construction. Philos. Trans. R. Soc. Lond. 30, 202–218 (1826)CrossRef
134.
J. Glover, A.C. Lazer, P.J. McKenna, Existence and stability of large scale nonlinear oscillations in suspension bridges. Zeit. Angew. Math. Phys. 40, 172–200 (1989)CrossRefMATHMathSciNet
143.
L.D Humphreys, P.J. McKenna, Multiple periodic solutions for a nonlinear suspension bridge equation. IMA J. Appl. Math. 63, 37–49 (1999)
144.
L.D. Humphreys, P.J. McKenna, When a mechanical model goes nonlinear: unexpected responses to low-periodic shaking. Am. Math. Mon. 112, 861–875 (2005)CrossRefMATHMathSciNet
145.
L.D. Humphreys, P.J. McKenna, K.M. O’Neill, High frequency shaking induced by low frequency forcing: periodic oscillations in a spring-cable system. Nonlinear Anal. Real World Appl. 11, 4312–4325 (2010)CrossRefMATHMathSciNet
146.
L.D. Humphreys, R. Shammas, Finding unpredictable behavior in a simple ordinary differential equation. Coll. Math. J. 31, 338–346 (2000)CrossRefMATHMathSciNet
147.
G.W. Hunt, H.M. Bolt, J.M.T. Thompson, Localisation and the dynamical phase-space analogy. Proc. R. Soc. Lond. A 425, 245–267 (1989)CrossRefMATHMathSciNet
153.
T. Kawada, History of the Modern Suspension Bridge: Solving the Dilemma Between Economy and Stiffness (ASCE Press, Reston, 2010)CrossRef
160.
161.
W. Lacarbonara, V. Colone, Dynamic response of arch bridges traversed by high-speed trains. J. Sound Vib. 304, 72–90 (2007)CrossRef
167.
A.C. Lazer, P.J. McKenna, Large scale oscillatory behaviour in loaded asymmetric systems. Ann. Inst. H. Poincaré Anal. Non Linear 4, 243–274 (1987)MATHMathSciNet
168.
A.C. Lazer, P.J. McKenna, Large-amplitude periodic oscillations in suspension bridges: some new connections with nonlinear analysis. SIAM Rev. 32, 537–578 (1990)CrossRefMATHMathSciNet
169.
A.C. Lazer, P.J. McKenna, On travelling waves in a suspension bridge model as the wave speed goes to zero. Nonlinear Anal. T.M.A. 74, 3998–4001 (2011)
175.
M.F. Liu, T.P. Chang, D.Y. Zeng, The interactive vibration behavior in a suspension bridge system under moving vehicle loads and vertical seismic excitations. Appl. Math. Model. 35, 398–411 (2011)CrossRefMATHMathSciNet
177.
J.L. Luco, J. Turmo, Effect of hanger flexibility on dynamic response of suspension bridges. J. Eng. Mech. 136, 1444–1459 (2010)CrossRef
187.
A. Matas, J. Očenášek, Modelling of suspension bridges. Proc. Comput. Mech. 2, 275–278 (2002)
196.
197.
199.
J. Melan, Theory of Arches and Suspension Bridges (Myron Clark, London, 1913). German original: Handbuch der Ingenieurwissenschaften, vol. 2 (1906)
201.
A.M. Micheletti, A. Pistoia, C. Saccon, Nontrivial solutions for a floating beam equation. Ricerche Mat. 48, 187–197 (1999)MATHMathSciNet
202.
A.M. Micheletti, C. Saccon, Multiple nontrivial solutions for a floating beam equation via critical point theory. J. Differ. Equ. 170, 157–179 (2001)CrossRefMATHMathSciNet
209.
C.L. Navier, Extraits des recherches sur la flexion des plans élastiques. Bulletin des Sciences de la Société Philomathique de Paris 92–102 (1823)
210.
C.L. Navier, Mémoire sur les ponts suspendus (Imprimerie Royale, Paris, 1823)
216.
L.A. Peletier, W.C. Troy, Spatial patterns, in Higher Order Models in Physics and Mechanics. Progress in Nonlinear Differential Equations and Their Applications, vol. 45 (Birkhäuser, Boston, 2001)
217.
221.
W. Podolny, Cable-Suspended Bridges, in Structural Steel Designer’s Handbook: AISC, AASHTO, AISI, ASTM, AREMA, and ASCE-07 Design Standards, ed. by R.L. Brockenbrough, F.S. Merritt, 5th edn. (McGraw-Hill, New York, 2011)
228.
P. Radu, D. Toundykov, J. Trageser, Finite time blow-up in nonlinear suspension bridges models. J. Differ. Equ. 257, 4030–4063 (2014)CrossRefMATHMathSciNet
229.
W.J.M. Rankine, A Manual of Applied Mechanics (Charles Griffin & Company, London, 1858)
233.
A.R. Robinson, H.H. West, A re-examination of the theory of suspension bridges. Civil Engineering Series, Structural Research Series no. 322, Doctoral Dissertation, Urbana, Illinois, 1967
234.
Y. Rocard, Dynamic Instability: Automobiles, Aircraft, Suspension Bridges (Crosby Lockwood, London, 1957)
239.
R.H. Scanlan, J.J. Tomko, Airfoil and bridge deck flutter derivatives. J. Eng. Mech. 97, 1717–1737 (1971)
241.
R. Scott, In the Wake of Tacoma: Suspension Bridges and the Quest for Aerodynamic Stability (ASCE Press, Reston, 2001)CrossRef
245.
F.C. Smith, G.S. Vincent, Aerodynamic Stability of Suspension Bridges: With Special Reference to the Tacoma Narrows Bridge, Part II: Mathematical Analysis. Investigation conducted by the Structural Research Laboratory, University of Washington (University of Washington Press, Seattle, 1950)
248.
D.B. Steinman, A Practical Treatise on Suspension Bridges, Their Design, Construction and Erection (Wiley, New York, 1922)
253.
257.
261.
S.P. Timoshenko, D.H. Young, Theory of Structures (McGraw-Hill Kogakusha, Tokyo, 1965)
279.
S. Woinowsky-Krieger, The effect of an axial force on the vibration of hinged bars. J. Appl. Mech. 17, 35–36 (1950)MATHMathSciNet
280.
G.P. Wollmann, Preliminary analysis of suspension bridges. J. Bridge Eng. 6, 227–233 (2001)CrossRef
Metadaten
Titel
One Dimensional Models
verfasst von
Filippo Gazzola
Copyright-Jahr
2015
Buch
Mathematical Models for Suspension Bridges

Print ISBN: 978-3-319-15433-6

Electronic ISBN: 978-3-319-15434-3

Copyright-Jahr: 2015

DOI
https://doi.org/10.1007/978-3-319-15434-3_2

Premium Partner

    Marktübersichten

    Die im Laufe eines Jahres in der „adhäsion“ veröffentlichten Marktübersichten helfen Anwendern verschiedenster Branchen, sich einen gezielten Überblick über Lieferantenangebote zu verschaffen. 

    Zur Marktübersicht
    Bildnachweise