Modeling suspension bridges through the von K\'arm\'an quasilinear plate equations

TL;DR

This paper models suspension bridge decks using the nonlinear von Kármán plate equations, analyzing oscillation modes and static equilibria to better understand their stability and behavior.

Contribution

It applies the von Kármán quasilinear plate model to suspension bridges, incorporating hanger effects and boundary conditions, and provides detailed analysis of oscillation modes and equilibrium states.

Findings

Detailed oscillation modes of the bridge deck are characterized.

Existence and multiplicity of static equilibria are established under various buckling load conditions.

The model enhances understanding of nonlinear oscillations in suspension bridges.

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 K\'arm\'an 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.