Long-Term Damped Dynamics of the Extensible Suspension Bridge

TL;DR

This paper analyzes the long-term behavior of an extensible suspension bridge modeled by a doubly nonlinear equation, establishing the existence of bounded absorbing sets and a global attractor under various conditions.

Contribution

It provides a rigorous mathematical analysis of the long-term dynamics of an extensible suspension bridge, including existence of attractors and steady states, for arbitrary loads and stiffness.

Findings

Existence of bounded absorbing sets for the system.

Presence of a global attractor with optimal regularity.

Characterization of steady states related to the attractor.

Abstract

This work is focused on the doubly nonlinear equation, whose solutions represent the bending motion of an extensible, elastic bridge suspended by continuously distributed cables which are flexible and elastic with stiffness k^2. When the ends are pinned, long-term dynamics is scrutinized for arbitrary values of axial load p and stiffness k^2. For a general external source f, we prove the existence of bounded absorbing sets.When f is timeindependent, the related semigroup of solutions is shown to possess the global attractor of optimal regularity and its characterization is given in terms of the steady states of the problem.