Long‐Term Damped Dynamics of the Extensible Suspension Bridge

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 . When the ends are pinned, long-term dynamics is scrutinized for arbitrary values of axial load and stiffness . For a general external source , we prove the existence of bounded absorbing sets. When is time-independent, 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.

Long-Term Dynamics of the Coupled Suspension Bridge System

“…5 we scrutinized the long-term dynamics of solutions to (1.3) for arbitrary values of p and k 2 . In particular, the existence of bounded absorbing sets has been proved for a general external source f .…”

Asymptotic dynamics of nonlinear coupled suspension bridge equations

“…By virtue of the interpolation inequality 6) taking into account (2.1) and Lemma 1, we easily obtain…”

“…When h = 0, it is apparent that functions F L and F OS , respectively, provide simple models of Linear and One-Sided springs with stiffness k 2 (see [6,8]). On the other hand, the dissipative terms appearing when h > 0 model some damping effect inside the springs.…”

“…Apart from a lot of works which deal with approximations and numerical simulations, some of them are devoted to scrutinize the periodic or longtime global dynamics by analytical methods [6,8,9,22,26].…”

Simplified Method of Determination of Natural-Vibration Frequencies of Prestressed Suspension Bridge

“…Analyses of natural-vibration frequencies of prestressed suspension structures are realized with labour-intensive discrete methods at present [21][22][23]. There is a lack of simple natural-vibration frequency determination methods, which can be used for approximate design.…”