Instability of modes in a partially hinged rectangular plate

TL;DR

This paper analyzes the stability of modes in a partially hinged rectangular bridge deck modeled by a nonlocal evolution equation, providing theoretical results and numerical experiments to understand mode instability phenomena.

Contribution

It introduces a mathematical model for a partially hinged rectangular plate and proves existence, uniqueness, and stability results for its solutions, including mode stability analysis.

Findings

Identification of conditions for mode stability and instability

Numerical validation of theoretical stability results

Insights into bridge deck mode behavior

Abstract

We consider a thin and narrow rectangular plate where the two short edges are hinged whereas the two long edges are free. This plate aims to represent the deck of a bridge, either a footbridge or a suspension bridge. We study a nonlocal evolution equation modeling the deformation of the plate and we prove existence, uniqueness and asymptotic behavior for the solutions for all initial data in suitable functional spaces. Then we prove results on the stability/instability of simple modes motivated by a phenomenon which is visible in actual bridges and we complement these theorems with some numerical experiments.