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Modeling suspension bridges through the von Kármán quasilinear plate equations

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Contributions to Nonlinear Elliptic Equations and Systems

Part of the book series: Progress in Nonlinear Differential Equations and Their Applications ((PNLDE,volume 86))

Abstract

A rectangular plate modeling the deck of a suspension bridge is considered. The plate may widely oscillate, which suggests to consider models from nonlinear elasticity. The von Kármán plate model is studied, complemented with the action of the hangers and with suitable boundary conditions describing the behavior of the deck. The oscillating modes are determined in full detail. Existence and multiplicity of static equilibria are then obtained under different assumptions on the strength of the buckling load.

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Authors and Affiliations

  1. Dipartimento di Matematica, Politecnico di Milano, Milano, Italy

    Filippo Gazzola & Yongda Wang

Authors
  1. Filippo Gazzola
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  2. Yongda Wang
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Corresponding author

Correspondence to Filippo Gazzola .

Editor information

Editors and Affiliations

  1. Universidade de São Paulo, Instituto de Ciências Matemáticas e de Computação, São Carlos, São Paulo, Brazil

    Alexandre Nolasco de Carvalho

  2. Dipartimento di Matematica, Università degli Studi di Milano, Lombardia, Milano, Italy

    Bernhard Ruf

  3. Universidade de São Paulo, Instituto de Ciências Matemáticas e de Computação, São Carlos, São Paulo, Brazil

    Ederson Moreira dos Santos

  4. Département de Mathématique. CP 214, Université Libre de Bruxelles, Brussels, Belgium

    Jean-Pierre Gossez

  5. Universidade de São Paulo, Instituto de Ciências Matemáticas e de Computação, São Carlos, São Paulo, Brazil

    Sergio Henrique Monari Soares

  6. Université Pierre et Marie Curie, Laboratoire Jacques-Louis Lions, Paris, Paris, France

    Thierry Cazenave

Additional information

Dedicated to Djairo Guedes de Figueiredo, on the occasion of his 80th birthday

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Gazzola, F., Wang, Y. (2015). Modeling suspension bridges through the von Kármán quasilinear plate equations. In: Nolasco de Carvalho, A., Ruf, B., Moreira dos Santos, E., Gossez, JP., Monari Soares, S., Cazenave, T. (eds) Contributions to Nonlinear Elliptic Equations and Systems. Progress in Nonlinear Differential Equations and Their Applications, vol 86. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-19902-3_18

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