Periodic response and stability analysis of vibro-impact systems by an enriched harmonic balance method.
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| Title: | Periodic response and stability analysis of vibro-impact systems by an enriched harmonic balance method. |
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| Authors: | Zhou, Yu1 (AUTHOR), Wang, Li1 (AUTHOR), Huang, Jianliang1 (AUTHOR) huangjl@mail.sysu.edu.cn |
| Source: | Applied Mathematics & Mechanics. May2025, Vol. 46 Issue 5, p907-926. 20p. |
| Subjects: | Floquet theory, Backlash (Engineering), Elastic scattering, Runge-Kutta formulas, Rigid bodies |
| Abstract: | A vibro-impact system is a hot topic in the study on nonlinear dynamics due to its generality and importance in engineering. In general, the alternating frequency-time harmonic balance (AFT-HB) method can be used to solve elastic collision. However, since the system is non-smooth, the required Fourier/harmonic truncation order is high in order to achieve the theoretical convergence rate, resulting in expensive computational cost. Furthermore, for rigid body collision, the periodic response of the system cannot be solved with the AFT-HB method due to the discontinuous velocity of the system. In order to accelerate the convergence and solve highly non-smooth systems, an enriched harmonic balance (HB) method is proposed, which is derived from the AFT-HB method in the framework of event-driven Gauss quadrature. The basic idea is to augment the Fourier bases by introducing a non-smooth Bernoulli base such that the non-smooth Bernoulli base compensates for the non-smooth part of the solution and the smooth part of the solution is approximated by the Fourier bases, thus achieving accelerated convergence. Based on the enriched HB method, gear pair systems with gear backlash and oscillator systems with rigid impact are solved, and the dynamic response characteristics are analyzed in this work. Then, based on the Floquet theory, the event-driven monodromy matrix method for non-smooth systems is used to analyze the stability and bifurcation of the periodic solutions. The numerical example shows that the results obtained from the enriched HB method are consistent with those from the Runge-Kutta method, which proves that the presented method is an effective method for analyzing the dynamic response characteristic of the vibro-impact system. [ABSTRACT FROM AUTHOR] |
| Copyright of Applied Mathematics & Mechanics is the property of Springer Nature 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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| Items | – Name: Title Label: Title Group: Ti Data: Periodic response and stability analysis of vibro-impact systems by an enriched harmonic balance method. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Zhou%2C+Yu%22">Zhou, Yu</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Wang%2C+Li%22">Wang, Li</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Huang%2C+Jianliang%22">Huang, Jianliang</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> huangjl@mail.sysu.edu.cn</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Applied+Mathematics+%26+Mechanics%22">Applied Mathematics & Mechanics</searchLink>. May2025, Vol. 46 Issue 5, p907-926. 20p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Floquet+theory%22">Floquet theory</searchLink><br /><searchLink fieldCode="DE" term="%22Backlash+%28Engineering%29%22">Backlash (Engineering)</searchLink><br /><searchLink fieldCode="DE" term="%22Elastic+scattering%22">Elastic scattering</searchLink><br /><searchLink fieldCode="DE" term="%22Runge-Kutta+formulas%22">Runge-Kutta formulas</searchLink><br /><searchLink fieldCode="DE" term="%22Rigid+bodies%22">Rigid bodies</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: A vibro-impact system is a hot topic in the study on nonlinear dynamics due to its generality and importance in engineering. In general, the alternating frequency-time harmonic balance (AFT-HB) method can be used to solve elastic collision. However, since the system is non-smooth, the required Fourier/harmonic truncation order is high in order to achieve the theoretical convergence rate, resulting in expensive computational cost. Furthermore, for rigid body collision, the periodic response of the system cannot be solved with the AFT-HB method due to the discontinuous velocity of the system. In order to accelerate the convergence and solve highly non-smooth systems, an enriched harmonic balance (HB) method is proposed, which is derived from the AFT-HB method in the framework of event-driven Gauss quadrature. The basic idea is to augment the Fourier bases by introducing a non-smooth Bernoulli base such that the non-smooth Bernoulli base compensates for the non-smooth part of the solution and the smooth part of the solution is approximated by the Fourier bases, thus achieving accelerated convergence. Based on the enriched HB method, gear pair systems with gear backlash and oscillator systems with rigid impact are solved, and the dynamic response characteristics are analyzed in this work. Then, based on the Floquet theory, the event-driven monodromy matrix method for non-smooth systems is used to analyze the stability and bifurcation of the periodic solutions. The numerical example shows that the results obtained from the enriched HB method are consistent with those from the Runge-Kutta method, which proves that the presented method is an effective method for analyzing the dynamic response characteristic of the vibro-impact system. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Applied Mathematics & Mechanics is the property of Springer Nature 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: 10.1007/s10483-025-3253-8 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 20 StartPage: 907 Subjects: – SubjectFull: Floquet theory Type: general – SubjectFull: Backlash (Engineering) Type: general – SubjectFull: Elastic scattering Type: general – SubjectFull: Runge-Kutta formulas Type: general – SubjectFull: Rigid bodies Type: general Titles: – TitleFull: Periodic response and stability analysis of vibro-impact systems by an enriched harmonic balance method. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Zhou, Yu – PersonEntity: Name: NameFull: Wang, Li – PersonEntity: Name: NameFull: Huang, Jianliang IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 05 Text: May2025 Type: published Y: 2025 Identifiers: – Type: issn-print Value: 02534827 Numbering: – Type: volume Value: 46 – Type: issue Value: 5 Titles: – TitleFull: Applied Mathematics & Mechanics Type: main |
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