Stochastic dispersion behavior and optimal design of locally resonant metamaterial nanobeams using nonlocal strain gradient theory.
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| Title: | Stochastic dispersion behavior and optimal design of locally resonant metamaterial nanobeams using nonlocal strain gradient theory. |
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| Authors: | Chatterjee, T.1 (AUTHOR), El-Borgi, S.2 (AUTHOR), Trabelssi, M.3,4 (AUTHOR), Friswell, M.I.1,5 (AUTHOR) m.i.friswell@swansea.ac.uk |
| Source: | Probabilistic Engineering Mechanics. Jul2025, Vol. 81, pN.PAG-N.PAG. 1p. |
| Subjects: | Machine learning, Gaussian processes, Metamaterials, Theory of wave motion, Stochastic processes, Strains & stresses (Mechanics), Multi-objective optimization |
| Abstract: | This study examines the stochastic response of a metamaterial (MM) nanobeam, focusing on bandgap formation and analyzed using machine learning. The nanobeam is modeled as an infinitely long Euler–Bernoulli beam with two length scale parameters: the nonlocal and strain gradient parameter. Periodically distributed linear resonators along its length introduce periodicity. The deterministic analysis is conducted by estimating bandgap edge frequencies using the dispersion of elastic waves in a representative unit cell. The impact of uncertainties on wave propagation behavior indicate that geometric properties predominantly influence variability in frequency response, followed by material properties, affecting the location and width of the bandgap. Scale dependent parameters, however, have a negligible effect. A Gaussian process (GP) surrogate model is employed to efficiently capture the stochastic behavior of the nanobeam. To highlight the utility of machine learning in computationally intensive tasks, a multi-objective optimization problem is formulated to tailor the bandgap features of the nanobeam. The offline-trained GP model yields a Pareto front of design configurations closely aligned with actual simulations, eliminating the need for repeated analyses during optimization. This surrogate based optimizer efficiently facilitates reverse engineering of MM designs for user defined wave dispersion characteristics, showcasing its potential for large scale optimization. Importantly, the stochastic dispersion framework grounded in nonlocal strain gradient theory can be directly applied to other periodic MM nanostructures. By varying unit cell configurations and materials within the same computational pipeline, new insights into bandgap emergence across applications ranging from phononic waveguides, nanoscale acoustic devices to structure–property relationships in next-generation MMs can be rapidly obtained. • Investigated stochastic bandgap behavior in nanobeams via machine learning. • Modeled nanobeams as nonlocal strain gradient beams with periodic resonators. • Analyzed effects of material, geometric, and scale uncertainties on bandgaps. • Applied Gaussian process modeling for efficient stochastic response analysis. • Optimized designs for tailored wave dispersion using multi-objective methods. [ABSTRACT FROM AUTHOR] |
| Copyright of Probabilistic Engineering Mechanics is the property of Elsevier B.V. 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: 187866310 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Stochastic dispersion behavior and optimal design of locally resonant metamaterial nanobeams using nonlocal strain gradient theory. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Chatterjee%2C+T%2E%22">Chatterjee, T.</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22El-Borgi%2C+S%2E%22">El-Borgi, S.</searchLink><relatesTo>2</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Trabelssi%2C+M%2E%22">Trabelssi, M.</searchLink><relatesTo>3,4</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Friswell%2C+M%2EI%2E%22">Friswell, M.I.</searchLink><relatesTo>1,5</relatesTo> (AUTHOR)<i> m.i.friswell@swansea.ac.uk</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Probabilistic+Engineering+Mechanics%22">Probabilistic Engineering Mechanics</searchLink>. Jul2025, Vol. 81, pN.PAG-N.PAG. 1p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Machine+learning%22">Machine learning</searchLink><br /><searchLink fieldCode="DE" term="%22Gaussian+processes%22">Gaussian processes</searchLink><br /><searchLink fieldCode="DE" term="%22Metamaterials%22">Metamaterials</searchLink><br /><searchLink fieldCode="DE" term="%22Theory+of+wave+motion%22">Theory of wave motion</searchLink><br /><searchLink fieldCode="DE" term="%22Stochastic+processes%22">Stochastic processes</searchLink><br /><searchLink fieldCode="DE" term="%22Strains+%26+stresses+%28Mechanics%29%22">Strains & stresses (Mechanics)</searchLink><br /><searchLink fieldCode="DE" term="%22Multi-objective+optimization%22">Multi-objective optimization</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: This study examines the stochastic response of a metamaterial (MM) nanobeam, focusing on bandgap formation and analyzed using machine learning. The nanobeam is modeled as an infinitely long Euler–Bernoulli beam with two length scale parameters: the nonlocal and strain gradient parameter. Periodically distributed linear resonators along its length introduce periodicity. The deterministic analysis is conducted by estimating bandgap edge frequencies using the dispersion of elastic waves in a representative unit cell. The impact of uncertainties on wave propagation behavior indicate that geometric properties predominantly influence variability in frequency response, followed by material properties, affecting the location and width of the bandgap. Scale dependent parameters, however, have a negligible effect. A Gaussian process (GP) surrogate model is employed to efficiently capture the stochastic behavior of the nanobeam. To highlight the utility of machine learning in computationally intensive tasks, a multi-objective optimization problem is formulated to tailor the bandgap features of the nanobeam. The offline-trained GP model yields a Pareto front of design configurations closely aligned with actual simulations, eliminating the need for repeated analyses during optimization. This surrogate based optimizer efficiently facilitates reverse engineering of MM designs for user defined wave dispersion characteristics, showcasing its potential for large scale optimization. Importantly, the stochastic dispersion framework grounded in nonlocal strain gradient theory can be directly applied to other periodic MM nanostructures. By varying unit cell configurations and materials within the same computational pipeline, new insights into bandgap emergence across applications ranging from phononic waveguides, nanoscale acoustic devices to structure–property relationships in next-generation MMs can be rapidly obtained. • Investigated stochastic bandgap behavior in nanobeams via machine learning. • Modeled nanobeams as nonlocal strain gradient beams with periodic resonators. • Analyzed effects of material, geometric, and scale uncertainties on bandgaps. • Applied Gaussian process modeling for efficient stochastic response analysis. • Optimized designs for tailored wave dispersion using multi-objective methods. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Probabilistic Engineering Mechanics is the property of Elsevier B.V. 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: 10.1016/j.probengmech.2025.103777 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 1 StartPage: N.PAG Subjects: – SubjectFull: Machine learning Type: general – SubjectFull: Gaussian processes Type: general – SubjectFull: Metamaterials Type: general – SubjectFull: Theory of wave motion Type: general – SubjectFull: Stochastic processes Type: general – SubjectFull: Strains & stresses (Mechanics) Type: general – SubjectFull: Multi-objective optimization Type: general Titles: – TitleFull: Stochastic dispersion behavior and optimal design of locally resonant metamaterial nanobeams using nonlocal strain gradient theory. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Chatterjee, T. – PersonEntity: Name: NameFull: El-Borgi, S. – PersonEntity: Name: NameFull: Trabelssi, M. – PersonEntity: Name: NameFull: Friswell, M.I. IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 07 Text: Jul2025 Type: published Y: 2025 Identifiers: – Type: issn-print Value: 02668920 Numbering: – Type: volume Value: 81 Titles: – TitleFull: Probabilistic Engineering Mechanics Type: main |
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