Investigation of critical speed of peripheral waves in beams under rotating load.

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Title: Investigation of critical speed of peripheral waves in beams under rotating load.
Authors: Dehghan, Ali1 (AUTHOR), Teymouri, Hadi1 (AUTHOR), Biglari, Hasan1 (AUTHOR) hbiglari@tabrizu.ac.ir
Source: Noise & Vibration Worldwide. Jun/Jul2026, Vol. 57 Issue 6/7, p573-583. 11p.
Subjects: Critical speeds (Engineering), Resonance, Dynamic stability, Rotor dynamics, Waves (Physics), Timoshenko beam theory, Mechanical engineering, Rotational motion
Abstract: This study presents a comprehensive investigation into the dynamic behaviour of a simply supported static shaft subjected to a rotating force at constant speed, formulated within the framework of Timoshenko beam theory. By employing energy-based methods, the governing system equations are derived and subsequently solved through a combination of Navier's analytical approach in the spatial domain and Newmark's numerical integration scheme in the time domain. The primary objective of this research is to identify and analyze the critical speed of peripheral waves generated in shafts under rotary moving forces, a phenomenon that poses significant challenges in the design of high-speed racing car tyres and other advanced mechanical systems. At the critical rotational speed, circumferential flexural waves resonate with the excitation, resulting in a continuous escalation of dynamic response and potential instability. The study further explores the influence of geometric and material parameters, including shaft slenderness ratio, force positioning, and material properties, on the onset of resonance. Comparative validation against existing analytical and numerical studies confirms the accuracy of the proposed methodology and highlights its applicability to practical engineering problems. The results reveal that steel demonstrates the highest critical rotational speed among the three materials examined, thereby reinforcing its suitability for high-speed applications where dynamic stability is essential. Overall, the findings contribute to a deeper understanding of shaft dynamics under rotary excitation and provide valuable insights for the optimization of mechanical components in automotive and aerospace engineering. [ABSTRACT FROM AUTHOR]
Copyright of Noise & Vibration Worldwide is the property of Sage Publications Inc. 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.)
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  Label: Title
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  Data: Investigation of critical speed of peripheral waves in beams under rotating load.
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  Data: <searchLink fieldCode="AR" term="%22Dehghan%2C+Ali%22">Dehghan, Ali</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Teymouri%2C+Hadi%22">Teymouri, Hadi</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Biglari%2C+Hasan%22">Biglari, Hasan</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> hbiglari@tabrizu.ac.ir</i>
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  Data: <searchLink fieldCode="JN" term="%22Noise+%26+Vibration+Worldwide%22">Noise & Vibration Worldwide</searchLink>. Jun/Jul2026, Vol. 57 Issue 6/7, p573-583. 11p.
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  Data: <searchLink fieldCode="DE" term="%22Critical+speeds+%28Engineering%29%22">Critical speeds (Engineering)</searchLink><br /><searchLink fieldCode="DE" term="%22Resonance%22">Resonance</searchLink><br /><searchLink fieldCode="DE" term="%22Dynamic+stability%22">Dynamic stability</searchLink><br /><searchLink fieldCode="DE" term="%22Rotor+dynamics%22">Rotor dynamics</searchLink><br /><searchLink fieldCode="DE" term="%22Waves+%28Physics%29%22">Waves (Physics)</searchLink><br /><searchLink fieldCode="DE" term="%22Timoshenko+beam+theory%22">Timoshenko beam theory</searchLink><br /><searchLink fieldCode="DE" term="%22Mechanical+engineering%22">Mechanical engineering</searchLink><br /><searchLink fieldCode="DE" term="%22Rotational+motion%22">Rotational motion</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: This study presents a comprehensive investigation into the dynamic behaviour of a simply supported static shaft subjected to a rotating force at constant speed, formulated within the framework of Timoshenko beam theory. By employing energy-based methods, the governing system equations are derived and subsequently solved through a combination of Navier's analytical approach in the spatial domain and Newmark's numerical integration scheme in the time domain. The primary objective of this research is to identify and analyze the critical speed of peripheral waves generated in shafts under rotary moving forces, a phenomenon that poses significant challenges in the design of high-speed racing car tyres and other advanced mechanical systems. At the critical rotational speed, circumferential flexural waves resonate with the excitation, resulting in a continuous escalation of dynamic response and potential instability. The study further explores the influence of geometric and material parameters, including shaft slenderness ratio, force positioning, and material properties, on the onset of resonance. Comparative validation against existing analytical and numerical studies confirms the accuracy of the proposed methodology and highlights its applicability to practical engineering problems. The results reveal that steel demonstrates the highest critical rotational speed among the three materials examined, thereby reinforcing its suitability for high-speed applications where dynamic stability is essential. Overall, the findings contribute to a deeper understanding of shaft dynamics under rotary excitation and provide valuable insights for the optimization of mechanical components in automotive and aerospace engineering. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Noise & Vibration Worldwide is the property of Sage Publications Inc. 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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        Value: 10.1177/09574565261419552
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      – Code: eng
        Text: English
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        PageCount: 11
        StartPage: 573
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      – SubjectFull: Critical speeds (Engineering)
        Type: general
      – SubjectFull: Resonance
        Type: general
      – SubjectFull: Dynamic stability
        Type: general
      – SubjectFull: Rotor dynamics
        Type: general
      – SubjectFull: Waves (Physics)
        Type: general
      – SubjectFull: Timoshenko beam theory
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      – SubjectFull: Mechanical engineering
        Type: general
      – SubjectFull: Rotational motion
        Type: general
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      – TitleFull: Investigation of critical speed of peripheral waves in beams under rotating load.
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            NameFull: Dehghan, Ali
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            NameFull: Teymouri, Hadi
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            NameFull: Biglari, Hasan
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            – D: 01
              M: 06
              Text: Jun/Jul2026
              Type: published
              Y: 2026
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              Value: 57
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              Value: 6/7
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