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Vibration analysis of beams with intermediate supports under moving loads.

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Title: Vibration analysis of beams with intermediate supports under moving loads.
Alternate Title: Hareketli yüklere maruz ayaklı kirişlerin titreşiminin incelenmesi.
Authors: Gemici, Emre1 gemici.e@gmail.com, Pala, Yaşar1 mypala@uludag.edu.tr
Source: Pamukkale University Journal of Engineering Sciences. 2025, Vol. 31 Issue 5, p744-749. 6p.
Subjects: Euler-Bernoulli beam theory, Dirac function, Series expansion (Mathematics), Girders, Mechanical vibration research, Live loads
Abstract: In this study, transverse vibration of a beam under a moving singular load and a moving moment is investigated. A simply supported beam with intermediate vertical supports modeled according to Euler-Bernoulli beam theory. The intermediate supports are modeled as consisting of a linear spring and a linear damper. The moving force and the moment, the spring force and the damper force are expressed using Dirac delta functions in the equations of motion. Obtaining the exact solution for this problem with classical methods are quite lengthy and complicated. Beam must be divided into spans between each support. Each span must be solved separately with different set of coordinates having same boundary conditions on support points. As the number of support increases, solution becomes more complicated. However, the present method can be used to solve the problem for the whole beam length without having to separate into various spans regardless of number of supports. Dirac delta functions are converted to series expansions which allows us to get exact solution in form of series expansion. This solution than can be easily calculated by a computer. Dynamic responses of several cases such as various number of supports; different support points; various moving load, moving moment and axial load combinations are examined. [ABSTRACT FROM AUTHOR]
Copyright of Pamukkale University Journal of Engineering Sciences is the property of Pamukkale University Journal of Engineering Sciences (PAJES) 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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DbLabel: Engineering Source
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  Data: Vibration analysis of beams with intermediate supports under moving loads.
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  Data: Hareketli yüklere maruz ayaklı kirişlerin titreşiminin incelenmesi.
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  Data: <searchLink fieldCode="AR" term="%22Gemici%2C+Emre%22">Gemici, Emre</searchLink><relatesTo>1</relatesTo><i> gemici.e@gmail.com</i><br /><searchLink fieldCode="AR" term="%22Pala%2C+Yaşar%22">Pala, Yaşar</searchLink><relatesTo>1</relatesTo><i> mypala@uludag.edu.tr</i>
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  Data: <searchLink fieldCode="JN" term="%22Pamukkale+University+Journal+of+Engineering+Sciences%22">Pamukkale University Journal of Engineering Sciences</searchLink>. 2025, Vol. 31 Issue 5, p744-749. 6p.
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  Data: <searchLink fieldCode="DE" term="%22Euler-Bernoulli+beam+theory%22">Euler-Bernoulli beam theory</searchLink><br /><searchLink fieldCode="DE" term="%22Dirac+function%22">Dirac function</searchLink><br /><searchLink fieldCode="DE" term="%22Series+expansion+%28Mathematics%29%22">Series expansion (Mathematics)</searchLink><br /><searchLink fieldCode="DE" term="%22Girders%22">Girders</searchLink><br /><searchLink fieldCode="DE" term="%22Mechanical+vibration+research%22">Mechanical vibration research</searchLink><br /><searchLink fieldCode="DE" term="%22Live+loads%22">Live loads</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: In this study, transverse vibration of a beam under a moving singular load and a moving moment is investigated. A simply supported beam with intermediate vertical supports modeled according to Euler-Bernoulli beam theory. The intermediate supports are modeled as consisting of a linear spring and a linear damper. The moving force and the moment, the spring force and the damper force are expressed using Dirac delta functions in the equations of motion. Obtaining the exact solution for this problem with classical methods are quite lengthy and complicated. Beam must be divided into spans between each support. Each span must be solved separately with different set of coordinates having same boundary conditions on support points. As the number of support increases, solution becomes more complicated. However, the present method can be used to solve the problem for the whole beam length without having to separate into various spans regardless of number of supports. Dirac delta functions are converted to series expansions which allows us to get exact solution in form of series expansion. This solution than can be easily calculated by a computer. Dynamic responses of several cases such as various number of supports; different support points; various moving load, moving moment and axial load combinations are examined. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Pamukkale University Journal of Engineering Sciences is the property of Pamukkale University Journal of Engineering Sciences (PAJES) 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.)
PLink https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=egs&AN=188590922
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      – Type: doi
        Value: 10.5505/pajes.2025.82596
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      – Code: eng
        Text: English
    PhysicalDescription:
      Pagination:
        PageCount: 6
        StartPage: 744
    Subjects:
      – SubjectFull: Euler-Bernoulli beam theory
        Type: general
      – SubjectFull: Dirac function
        Type: general
      – SubjectFull: Series expansion (Mathematics)
        Type: general
      – SubjectFull: Girders
        Type: general
      – SubjectFull: Mechanical vibration research
        Type: general
      – SubjectFull: Live loads
        Type: general
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      – TitleFull: Vibration analysis of beams with intermediate supports under moving loads.
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            NameFull: Gemici, Emre
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            NameFull: Pala, Yaşar
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            – D: 01
              M: 08
              Text: 2025
              Type: published
              Y: 2025
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            – TitleFull: Pamukkale University Journal of Engineering Sciences
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