STABILITY of A SUSPENSION BRIDGE with A LOCALIZED STRUCTURAL DAMPING

Zayd Hajjej; Mohammad Al-Gharabli; Salim Messaoudi

doi:10.3934/dcdss.2021089

STABILITY of A SUSPENSION BRIDGE with A LOCALIZED STRUCTURAL DAMPING

Zayd Hajjej
, Mohammad Al-Gharabli^*
, Salim Messaoudi

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

8 Scopus citations

Abstract

Strong vibrations can cause lots of damage to structures and break materials apart. The main reason for the Tacoma Narrows Bridge collapse was the sudden transition from longitudinal to torsional oscillations caused by a resonance phenomenon. There exist evidences that several other bridges collapsed for the same reason. To overcome unwanted vibrations and prevent structures from resonating during earthquakes, winds,..., features and modifications such as dampers are used to stabilize these bridges. In this work, we use a minimum amount of dissipation to establish exponential decay- rate estimates to the following nonlocal evolution equation utt(x, y, t) + ∆²u(x, y, t) − φ(u)uxx − (α(x, y)uxt(x, y, t))_x = 0, which models the deformation of the deck of either a footbridge or a suspension bridge.

Original language	English
Pages (from-to)	1165-1181
Number of pages	17
Journal	Discrete and Continuous Dynamical Systems - Series S
Volume	15
Issue number	5
DOIs	https://doi.org/10.3934/dcdss.2021089
State	Published - May 2022

Bibliographical note

Publisher Copyright:
© 2022 American Institute of Mathematical Sciences. All rights reserved.

Keywords

Suspension bridge
exponential decay
localized structural damping

ASJC Scopus subject areas

Analysis
Discrete Mathematics and Combinatorics
Applied Mathematics

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10.3934/dcdss.2021089

Cite this

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title = "STABILITY of A SUSPENSION BRIDGE with A LOCALIZED STRUCTURAL DAMPING",

abstract = "Strong vibrations can cause lots of damage to structures and break materials apart. The main reason for the Tacoma Narrows Bridge collapse was the sudden transition from longitudinal to torsional oscillations caused by a resonance phenomenon. There exist evidences that several other bridges collapsed for the same reason. To overcome unwanted vibrations and prevent structures from resonating during earthquakes, winds,..., features and modifications such as dampers are used to stabilize these bridges. In this work, we use a minimum amount of dissipation to establish exponential decay- rate estimates to the following nonlocal evolution equation utt(x, y, t) + ∆2u(x, y, t) − φ(u)uxx − (α(x, y)uxt(x, y, t))x = 0, which models the deformation of the deck of either a footbridge or a suspension bridge.",

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AU - Hajjej, Zayd

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PY - 2022/5

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AB - Strong vibrations can cause lots of damage to structures and break materials apart. The main reason for the Tacoma Narrows Bridge collapse was the sudden transition from longitudinal to torsional oscillations caused by a resonance phenomenon. There exist evidences that several other bridges collapsed for the same reason. To overcome unwanted vibrations and prevent structures from resonating during earthquakes, winds,..., features and modifications such as dampers are used to stabilize these bridges. In this work, we use a minimum amount of dissipation to establish exponential decay- rate estimates to the following nonlocal evolution equation utt(x, y, t) + ∆2u(x, y, t) − φ(u)uxx − (α(x, y)uxt(x, y, t))x = 0, which models the deformation of the deck of either a footbridge or a suspension bridge.

KW - Suspension bridge

KW - exponential decay

KW - localized structural damping

UR - https://www.scopus.com/pages/publications/85128271121

U2 - 10.3934/dcdss.2021089

DO - 10.3934/dcdss.2021089

M3 - Article

AN - SCOPUS:85128271121

SN - 1937-1632

VL - 15

SP - 1165

EP - 1181

JO - Discrete and Continuous Dynamical Systems - Series S

JF - Discrete and Continuous Dynamical Systems - Series S

IS - 5

ER -

STABILITY of A SUSPENSION BRIDGE with A LOCALIZED STRUCTURAL DAMPING

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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