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An effective strategy for time-stepping in dynamic systems with non-viscous damping.

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Title: An effective strategy for time-stepping in dynamic systems with non-viscous damping.
Authors: Ji, Yi1 (AUTHOR) jiyi@hit.edu.cn, Liu, Bo2 (AUTHOR) jiyi@hit.edu.cn, Wu, Yang3 (AUTHOR), Zhang, Huimin4 (AUTHOR)
Source: Journal of Vibration & Control. May2026, Vol. 32 Issue 9/10, p2524-2543. 20p.
Subjects: Time integration scheme, Damping (Mechanics), Energy dissipation, Dynamical systems, Dynamic stability, Numerical integration, Transient analysis
Abstract: This study develops a precise and reliable time-stepping strategy for evaluating the dynamic behavior of systems with non-viscous damping. The m -point interpolation quadrature method is designed to estimate the non-viscous damping force precisely, and the developed method can be applied to any kernel function. Additionally, to achieve reliable and precise dynamic responses, our research introduces a time integration method with three subs-steps, wherein algorithmic parameters are designed to keep some essential numerical properties. This paper gives the mathematical derivation and computational procedure of the three-sub-step method, and it thoroughly examines its numerical characteristics using a non-viscous damping model. Interestingly, through the theoretical analysis, it is evident that the chosen three-sub-step method has consistent stability, manageable dissipation, reliable stability, and excellent low-frequency precision. At the end of this paper, some representative non-viscous damping examples are conducted. Numerical results show that compared to the dynamic analysis strategies based on the currently popular time integration methods, under the same computations, our strategy enjoys superiorities both in stability, accuracy, and dissipation. [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: 193250575
AccessLevel: 6
PubType: Academic Journal
PubTypeId: academicJournal
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  Data: An effective strategy for time-stepping in dynamic systems with non-viscous damping.
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  Data: <searchLink fieldCode="AR" term="%22Ji%2C+Yi%22">Ji, Yi</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> jiyi@hit.edu.cn</i><br /><searchLink fieldCode="AR" term="%22Liu%2C+Bo%22">Liu, Bo</searchLink><relatesTo>2</relatesTo> (AUTHOR)<i> jiyi@hit.edu.cn</i><br /><searchLink fieldCode="AR" term="%22Wu%2C+Yang%22">Wu, Yang</searchLink><relatesTo>3</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Zhang%2C+Huimin%22">Zhang, Huimin</searchLink><relatesTo>4</relatesTo> (AUTHOR)
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  Data: <searchLink fieldCode="JN" term="%22Journal+of+Vibration+%26+Control%22">Journal of Vibration & Control</searchLink>. May2026, Vol. 32 Issue 9/10, p2524-2543. 20p.
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  Data: <searchLink fieldCode="DE" term="%22Time+integration+scheme%22">Time integration scheme</searchLink><br /><searchLink fieldCode="DE" term="%22Damping+%28Mechanics%29%22">Damping (Mechanics)</searchLink><br /><searchLink fieldCode="DE" term="%22Energy+dissipation%22">Energy dissipation</searchLink><br /><searchLink fieldCode="DE" term="%22Dynamical+systems%22">Dynamical systems</searchLink><br /><searchLink fieldCode="DE" term="%22Dynamic+stability%22">Dynamic stability</searchLink><br /><searchLink fieldCode="DE" term="%22Numerical+integration%22">Numerical integration</searchLink><br /><searchLink fieldCode="DE" term="%22Transient+analysis%22">Transient analysis</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: This study develops a precise and reliable time-stepping strategy for evaluating the dynamic behavior of systems with non-viscous damping. The m -point interpolation quadrature method is designed to estimate the non-viscous damping force precisely, and the developed method can be applied to any kernel function. Additionally, to achieve reliable and precise dynamic responses, our research introduces a time integration method with three subs-steps, wherein algorithmic parameters are designed to keep some essential numerical properties. This paper gives the mathematical derivation and computational procedure of the three-sub-step method, and it thoroughly examines its numerical characteristics using a non-viscous damping model. Interestingly, through the theoretical analysis, it is evident that the chosen three-sub-step method has consistent stability, manageable dissipation, reliable stability, and excellent low-frequency precision. At the end of this paper, some representative non-viscous damping examples are conducted. Numerical results show that compared to the dynamic analysis strategies based on the currently popular time integration methods, under the same computations, our strategy enjoys superiorities both in stability, accuracy, and dissipation. [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:
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    Identifiers:
      – Type: doi
        Value: 10.1177/10775463251333169
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      – Code: eng
        Text: English
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        PageCount: 20
        StartPage: 2524
    Subjects:
      – SubjectFull: Time integration scheme
        Type: general
      – SubjectFull: Damping (Mechanics)
        Type: general
      – SubjectFull: Energy dissipation
        Type: general
      – SubjectFull: Dynamical systems
        Type: general
      – SubjectFull: Dynamic stability
        Type: general
      – SubjectFull: Numerical integration
        Type: general
      – SubjectFull: Transient analysis
        Type: general
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      – TitleFull: An effective strategy for time-stepping in dynamic systems with non-viscous damping.
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            NameFull: Ji, Yi
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            NameFull: Liu, Bo
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            NameFull: Wu, Yang
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            NameFull: Zhang, Huimin
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            – D: 01
              M: 05
              Text: May2026
              Type: published
              Y: 2026
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              Value: 32
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              Value: 9/10
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            – TitleFull: Journal of Vibration & Control
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