Piecewise-Linear Approximation and Global Perturbation of Homoclinic Motions for a Two-Degree-of-Freedom Coupled Mechanical System.
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| Title: | Piecewise-Linear Approximation and Global Perturbation of Homoclinic Motions for a Two-Degree-of-Freedom Coupled Mechanical System. |
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| Authors: | Kou, Liying1 (AUTHOR) liykou@163.com, Xu, Rui1 (AUTHOR) xurtysx@163.com, Jia, Lele2 (AUTHOR) jialelesx@163.com, Li, Shuangbao1 (AUTHOR) shuangbaoli@yeah.net |
| Source: | International Journal of Bifurcation & Chaos in Applied Sciences & Engineering. Mar2026, Vol. 36 Issue 4, p1-25. 25p. |
| Subjects: | Piecewise linear approximation, Perturbation theory, Nonlinear oscillators, Dynamical systems, Chaos theory |
| Abstract: | In this paper, a novel two-degree-of-freedom mechanical system under sinusoidal excitation is established by coupling the archetypal Smooth and Discontinuous (SD) oscillator with a harmonic oscillator to analytically study the global perturbation dynamics of homoclinic motions. First, a piecewise-linear approximation of the irrational restoring force induced by the SD oscillator is carried out to reconstruct a four-dimensional piecewise-smooth nonautonomous system with a saddle-center geometrical structure. Second, the Melnikov method for piecewise-defined homoclinic orbits under periodic perturbation in the four-dimensional phase space is generalized to obtain the parameter threshold of chaos. Third, the effectiveness of this global perturbation technique is verified by numerical simulations, through which the regulation of the coupled system's dynamic response from both damping and periodic external excitation is revealed, along with the observation of rich nonlinear dynamic phenomena induced by their combined effects. Finally, a novel strategy is proposed to control the chaotic motion of the SD oscillator through a linear spring-coupled harmonic oscillator. The dynamic response analysis demonstrates that this coupled system enables passive vibration control of the SD oscillator, establishing a foundation for optimizing vibration absorber designs. [ABSTRACT FROM AUTHOR] |
| Copyright of International Journal of Bifurcation & Chaos in Applied Sciences & Engineering is the property of World Scientific Publishing Company 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 |
| FullText | Text: Availability: 0 |
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| Header | DbId: egs DbLabel: Engineering Source An: 191379137 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Piecewise-Linear Approximation and Global Perturbation of Homoclinic Motions for a Two-Degree-of-Freedom Coupled Mechanical System. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Kou%2C+Liying%22">Kou, Liying</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> liykou@163.com</i><br /><searchLink fieldCode="AR" term="%22Xu%2C+Rui%22">Xu, Rui</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> xurtysx@163.com</i><br /><searchLink fieldCode="AR" term="%22Jia%2C+Lele%22">Jia, Lele</searchLink><relatesTo>2</relatesTo> (AUTHOR)<i> jialelesx@163.com</i><br /><searchLink fieldCode="AR" term="%22Li%2C+Shuangbao%22">Li, Shuangbao</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> shuangbaoli@yeah.net</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22International+Journal+of+Bifurcation+%26+Chaos+in+Applied+Sciences+%26+Engineering%22">International Journal of Bifurcation & Chaos in Applied Sciences & Engineering</searchLink>. Mar2026, Vol. 36 Issue 4, p1-25. 25p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Piecewise+linear+approximation%22">Piecewise linear approximation</searchLink><br /><searchLink fieldCode="DE" term="%22Perturbation+theory%22">Perturbation theory</searchLink><br /><searchLink fieldCode="DE" term="%22Nonlinear+oscillators%22">Nonlinear oscillators</searchLink><br /><searchLink fieldCode="DE" term="%22Dynamical+systems%22">Dynamical systems</searchLink><br /><searchLink fieldCode="DE" term="%22Chaos+theory%22">Chaos theory</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: In this paper, a novel two-degree-of-freedom mechanical system under sinusoidal excitation is established by coupling the archetypal Smooth and Discontinuous (SD) oscillator with a harmonic oscillator to analytically study the global perturbation dynamics of homoclinic motions. First, a piecewise-linear approximation of the irrational restoring force induced by the SD oscillator is carried out to reconstruct a four-dimensional piecewise-smooth nonautonomous system with a saddle-center geometrical structure. Second, the Melnikov method for piecewise-defined homoclinic orbits under periodic perturbation in the four-dimensional phase space is generalized to obtain the parameter threshold of chaos. Third, the effectiveness of this global perturbation technique is verified by numerical simulations, through which the regulation of the coupled system's dynamic response from both damping and periodic external excitation is revealed, along with the observation of rich nonlinear dynamic phenomena induced by their combined effects. Finally, a novel strategy is proposed to control the chaotic motion of the SD oscillator through a linear spring-coupled harmonic oscillator. The dynamic response analysis demonstrates that this coupled system enables passive vibration control of the SD oscillator, establishing a foundation for optimizing vibration absorber designs. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of International Journal of Bifurcation & Chaos in Applied Sciences & Engineering is the property of World Scientific Publishing Company 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: 10.1142/S0218127426500422 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 25 StartPage: 1 Subjects: – SubjectFull: Piecewise linear approximation Type: general – SubjectFull: Perturbation theory Type: general – SubjectFull: Nonlinear oscillators Type: general – SubjectFull: Dynamical systems Type: general – SubjectFull: Chaos theory Type: general Titles: – TitleFull: Piecewise-Linear Approximation and Global Perturbation of Homoclinic Motions for a Two-Degree-of-Freedom Coupled Mechanical System. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Kou, Liying – PersonEntity: Name: NameFull: Xu, Rui – PersonEntity: Name: NameFull: Jia, Lele – PersonEntity: Name: NameFull: Li, Shuangbao IsPartOfRelationships: – BibEntity: Dates: – D: 30 M: 03 Text: Mar2026 Type: published Y: 2026 Identifiers: – Type: issn-print Value: 02181274 Numbering: – Type: volume Value: 36 – Type: issue Value: 4 Titles: – TitleFull: International Journal of Bifurcation & Chaos in Applied Sciences & Engineering Type: main |
| ResultId | 1 |
