Optimization of cantilever beams with multiple flexoelectric actuators based on Newton–Raphson iteration.
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| Title: | Optimization of cantilever beams with multiple flexoelectric actuators based on Newton–Raphson iteration. |
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| Authors: | Li, Yiming1 (AUTHOR) 052010212@nuaa.edu.cn, Chen, Chen1 (AUTHOR) SX2301068@nuaa.edu.cn, Fan, Mu1 (AUTHOR) mfanz@nuaa.edu.cn |
| Source: | Acta Mechanica. Feb2026, Vol. 237 Issue 2, p599-615. 17p. |
| Subjects: | Newton-Raphson method, Flexoelectricity, Mechanical behavior of materials, Nanoelectromechanical systems, Cantilevers, Multi-objective optimization, Atomic force microscopes, Active noise & vibration control |
| Abstract: | This study delves into the complexity of optimizing multiple actuators on a cantilever beam, focusing on the flexoelectric effect caused by the non-uniform electric field generated by an atomic force microscope (AFM) probe. Multiple actuators control has significant research value in enhancing the flexoelectric effect, greatly alleviating stress concentration and achieving precise vibration control. The current challenge in multiple flexoelectric actuators research is multi-objective optimization, addressed here using the Newton–Raphson iterative method, known for its robustness in the convex function domain, as an optimization framework. By analyzing structural parameters and flexoelectric actuator parameters, significant influencing factors are selected to form the vector space, determining actuator positions and driving voltages. These variables constitute the optimization space and are incorporated into the Newton–Raphson general iterative equation to derive the iteration matrix, which is computed using MATLAB. Case studies confirm that the Newton–Raphson method effectively identifies optimal actuator positions and driving voltages at different modes without external force, significantly improving flexoelectric control efficiency. Additionally, it quickly stabilizes vibrations at different modes under external force. However, the study has limitations, as the Newton–Raphson method cannot effectively solve non-convex function optimization in linear space. This research advances the understanding of multiple actuators optimization control structure dynamics and promotes the development of more effective engineering solutions, particularly in achieving more precise actuation and control in the field of micro- and nano-structure engineering. [ABSTRACT FROM AUTHOR] |
| Copyright of Acta Mechanica 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.) | |
| Database: | Engineering Source |
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| Header | DbId: egs DbLabel: Engineering Source An: 191605763 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Optimization of cantilever beams with multiple flexoelectric actuators based on Newton–Raphson iteration. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Li%2C+Yiming%22">Li, Yiming</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> 052010212@nuaa.edu.cn</i><br /><searchLink fieldCode="AR" term="%22Chen%2C+Chen%22">Chen, Chen</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> SX2301068@nuaa.edu.cn</i><br /><searchLink fieldCode="AR" term="%22Fan%2C+Mu%22">Fan, Mu</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> mfanz@nuaa.edu.cn</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Acta+Mechanica%22">Acta Mechanica</searchLink>. Feb2026, Vol. 237 Issue 2, p599-615. 17p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Newton-Raphson+method%22">Newton-Raphson method</searchLink><br /><searchLink fieldCode="DE" term="%22Flexoelectricity%22">Flexoelectricity</searchLink><br /><searchLink fieldCode="DE" term="%22Mechanical+behavior+of+materials%22">Mechanical behavior of materials</searchLink><br /><searchLink fieldCode="DE" term="%22Nanoelectromechanical+systems%22">Nanoelectromechanical systems</searchLink><br /><searchLink fieldCode="DE" term="%22Cantilevers%22">Cantilevers</searchLink><br /><searchLink fieldCode="DE" term="%22Multi-objective+optimization%22">Multi-objective optimization</searchLink><br /><searchLink fieldCode="DE" term="%22Atomic+force+microscopes%22">Atomic force microscopes</searchLink><br /><searchLink fieldCode="DE" term="%22Active+noise+%26+vibration+control%22">Active noise & vibration control</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: This study delves into the complexity of optimizing multiple actuators on a cantilever beam, focusing on the flexoelectric effect caused by the non-uniform electric field generated by an atomic force microscope (AFM) probe. Multiple actuators control has significant research value in enhancing the flexoelectric effect, greatly alleviating stress concentration and achieving precise vibration control. The current challenge in multiple flexoelectric actuators research is multi-objective optimization, addressed here using the Newton–Raphson iterative method, known for its robustness in the convex function domain, as an optimization framework. By analyzing structural parameters and flexoelectric actuator parameters, significant influencing factors are selected to form the vector space, determining actuator positions and driving voltages. These variables constitute the optimization space and are incorporated into the Newton–Raphson general iterative equation to derive the iteration matrix, which is computed using MATLAB. Case studies confirm that the Newton–Raphson method effectively identifies optimal actuator positions and driving voltages at different modes without external force, significantly improving flexoelectric control efficiency. Additionally, it quickly stabilizes vibrations at different modes under external force. However, the study has limitations, as the Newton–Raphson method cannot effectively solve non-convex function optimization in linear space. This research advances the understanding of multiple actuators optimization control structure dynamics and promotes the development of more effective engineering solutions, particularly in achieving more precise actuation and control in the field of micro- and nano-structure engineering. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Acta Mechanica 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/s00707-024-04085-9 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 17 StartPage: 599 Subjects: – SubjectFull: Newton-Raphson method Type: general – SubjectFull: Flexoelectricity Type: general – SubjectFull: Mechanical behavior of materials Type: general – SubjectFull: Nanoelectromechanical systems Type: general – SubjectFull: Cantilevers Type: general – SubjectFull: Multi-objective optimization Type: general – SubjectFull: Atomic force microscopes Type: general – SubjectFull: Active noise & vibration control Type: general Titles: – TitleFull: Optimization of cantilever beams with multiple flexoelectric actuators based on Newton–Raphson iteration. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Li, Yiming – PersonEntity: Name: NameFull: Chen, Chen – PersonEntity: Name: NameFull: Fan, Mu IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 02 Text: Feb2026 Type: published Y: 2026 Identifiers: – Type: issn-print Value: 00015970 Numbering: – Type: volume Value: 237 – Type: issue Value: 2 Titles: – TitleFull: Acta Mechanica Type: main |
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