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Interval dynamic responses analysis of the damaged arch with uncertainties subjected to a moving load.

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Title: Interval dynamic responses analysis of the damaged arch with uncertainties subjected to a moving load.
Authors: Nie, Zhihua1,2 (AUTHOR), Fu, Chao1 (AUTHOR) fuchao@nwpu.edu.cn, Yang, Yongfeng1 (AUTHOR)
Source: Journal of Vibration & Control. Aug2026, Vol. 32 Issue 15/16, p4419-4434. 16p.
Subjects: Differential quadrature method, Interval analysis, Parameterization, Dynamical systems, Chebyshev polynomials, Live loads, Arch bridges
Abstract: This paper focuses on the interval dynamic response of a damaged arch with uncertain parameters under a moving load. The differential quadrature method (DQM) is employed to derive the equation of motion of the arch. The moving load, modeled as the Dirac delta function, is approximated by a Fourier trigonometric series to tackle the issue of discretizing the singular function in the differential equation. The bending moment at each discrete point is obtained via the equilibrium equation. The damage in the arch is modeled as the cross-section reduction model. The Newmark-β method is then used to obtain the dynamic response. Moreover, uncertain damage-related parameters of the arch are treated as interval variables, and the Chebyshev polynomial surrogate model is utilized to obtain the interval dynamic response, followed by a comparison with the deterministic one. The results obtained from our study address the question of how to accurately analyze the interval dynamic response of damaged arches with uncertain parameters under a moving load, which can offer valuable references for the design and assessment of arch structures. [ABSTRACT FROM AUTHOR]
Copyright of Journal of Vibration & Control is the property of Sage Publications, Ltd. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
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Header DbId: egs
DbLabel: Engineering Source
An: 195315256
AccessLevel: 6
PubType: Academic Journal
PubTypeId: academicJournal
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  Data: Interval dynamic responses analysis of the damaged arch with uncertainties subjected to a moving load.
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  Data: <searchLink fieldCode="AR" term="%22Nie%2C+Zhihua%22">Nie, Zhihua</searchLink><relatesTo>1,2</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Fu%2C+Chao%22">Fu, Chao</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> fuchao@nwpu.edu.cn</i><br /><searchLink fieldCode="AR" term="%22Yang%2C+Yongfeng%22">Yang, Yongfeng</searchLink><relatesTo>1</relatesTo> (AUTHOR)
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  Data: <searchLink fieldCode="JN" term="%22Journal+of+Vibration+%26+Control%22">Journal of Vibration & Control</searchLink>. Aug2026, Vol. 32 Issue 15/16, p4419-4434. 16p.
– Name: Subject
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  Data: <searchLink fieldCode="DE" term="%22Differential+quadrature+method%22">Differential quadrature method</searchLink><br /><searchLink fieldCode="DE" term="%22Interval+analysis%22">Interval analysis</searchLink><br /><searchLink fieldCode="DE" term="%22Parameterization%22">Parameterization</searchLink><br /><searchLink fieldCode="DE" term="%22Dynamical+systems%22">Dynamical systems</searchLink><br /><searchLink fieldCode="DE" term="%22Chebyshev+polynomials%22">Chebyshev polynomials</searchLink><br /><searchLink fieldCode="DE" term="%22Live+loads%22">Live loads</searchLink><br /><searchLink fieldCode="DE" term="%22Arch+bridges%22">Arch bridges</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: This paper focuses on the interval dynamic response of a damaged arch with uncertain parameters under a moving load. The differential quadrature method (DQM) is employed to derive the equation of motion of the arch. The moving load, modeled as the Dirac delta function, is approximated by a Fourier trigonometric series to tackle the issue of discretizing the singular function in the differential equation. The bending moment at each discrete point is obtained via the equilibrium equation. The damage in the arch is modeled as the cross-section reduction model. The Newmark-β method is then used to obtain the dynamic response. Moreover, uncertain damage-related parameters of the arch are treated as interval variables, and the Chebyshev polynomial surrogate model is utilized to obtain the interval dynamic response, followed by a comparison with the deterministic one. The results obtained from our study address the question of how to accurately analyze the interval dynamic response of damaged arches with uncertain parameters under a moving load, which can offer valuable references for the design and assessment of arch structures. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Journal of Vibration & Control is the property of Sage Publications, Ltd. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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RecordInfo BibRecord:
  BibEntity:
    Identifiers:
      – Type: doi
        Value: 10.1177/10775463251361336
    Languages:
      – Code: eng
        Text: English
    PhysicalDescription:
      Pagination:
        PageCount: 16
        StartPage: 4419
    Subjects:
      – SubjectFull: Differential quadrature method
        Type: general
      – SubjectFull: Interval analysis
        Type: general
      – SubjectFull: Parameterization
        Type: general
      – SubjectFull: Dynamical systems
        Type: general
      – SubjectFull: Chebyshev polynomials
        Type: general
      – SubjectFull: Live loads
        Type: general
      – SubjectFull: Arch bridges
        Type: general
    Titles:
      – TitleFull: Interval dynamic responses analysis of the damaged arch with uncertainties subjected to a moving load.
        Type: main
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          Name:
            NameFull: Nie, Zhihua
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          Name:
            NameFull: Fu, Chao
      – PersonEntity:
          Name:
            NameFull: Yang, Yongfeng
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          Dates:
            – D: 01
              M: 08
              Text: Aug2026
              Type: published
              Y: 2026
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              Value: 10775463
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              Value: 32
            – Type: issue
              Value: 15/16
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            – TitleFull: Journal of Vibration & Control
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