On a nonlinear nonlocal hyperbolic system modeling suspension bridges

TL;DR

This paper introduces a new nonlinear nonlocal hyperbolic model for suspension bridge dynamics, capturing the interactions of the deck, cables, and hangers, with proven existence and uniqueness of solutions.

Contribution

It develops a novel mathematical model based on variational principles for suspension bridges, including rigorous analysis of well-posedness.

Findings

Derivation of a coupled nonlinear hyperbolic system from physical principles

Proof of existence and uniqueness of solutions for the model

Energy balance analysis confirming model consistency

Abstract

We suggest a new model for the dynamics of a suspension bridge through a system of nonlinear nonlocal hyperbolic differential equations. The equations are of second and fourth order in space and describe the behavior of the main components of the bridge: the deck, the sustaining cables and the connecting hangers. We perform a careful energy balance and we derive the equations from a variational principle. We then prove existence and uniqueness for the resulting problem.