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Stochastic dispersion behavior and optimal design of locally resonant metamaterial nanobeams using nonlocal strain gradient theory

T. Chatterjee, S. El-Borgi, M. Trabelssi, Michael Friswell

Probabilistic Engineering Mechanics, Volume: 81, Start page: 103777

Swansea University Author: Michael Friswell

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DOI (Published version): 10.1016/j.probengmech.2025.103777

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. Periodicall...

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Published in: Probabilistic Engineering Mechanics
ISSN: 0266-8920 1878-4275
Published: Elsevier BV 2025
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URI: https://cronfa.swan.ac.uk/Record/cronfa69647
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last_indexed 2025-06-26T06:48:06Z
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spelling 2025-06-25T11:32:58.2785734 v2 69647 2025-06-09 Stochastic dispersion behavior and optimal design of locally resonant metamaterial nanobeams using nonlocal strain gradient theory 5894777b8f9c6e64bde3568d68078d40 Michael Friswell Michael Friswell true false 2025-06-09 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. Journal Article Probabilistic Engineering Mechanics 81 103777 Elsevier BV 0266-8920 1878-4275 Metamaterial nanobeam; Bandgap; Nonlocal strain gradient theory; Stochastic response analysis; Gaussian process modeling; Multi-objective optimization 1 7 2025 2025-07-01 10.1016/j.probengmech.2025.103777 COLLEGE NANME COLLEGE CODE Swansea University SU Library paid the OA fee (TA Institutional Deal) The first author gratefully acknowledges the support of the University of Surrey through the award of a faculty start-up grant. 2025-06-25T11:32:58.2785734 2025-06-09T10:01:22.3527901 Faculty of Science and Engineering School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Aerospace Engineering T. Chatterjee 1 S. El-Borgi 2 M. Trabelssi 3 Michael Friswell 4 69647__34579__1fee9c66020f4c48b805de0763c8e1c0.pdf 69647.VOR.pdf 2025-06-25T11:30:13.3433538 Output 3283762 application/pdf Version of Record true © 2025 The Authors. This is an open access article under the CC BY license. true eng http://creativecommons.org/licenses/by/4.0/
title Stochastic dispersion behavior and optimal design of locally resonant metamaterial nanobeams using nonlocal strain gradient theory
spellingShingle Stochastic dispersion behavior and optimal design of locally resonant metamaterial nanobeams using nonlocal strain gradient theory
Michael Friswell
title_short Stochastic dispersion behavior and optimal design of locally resonant metamaterial nanobeams using nonlocal strain gradient theory
title_full Stochastic dispersion behavior and optimal design of locally resonant metamaterial nanobeams using nonlocal strain gradient theory
title_fullStr Stochastic dispersion behavior and optimal design of locally resonant metamaterial nanobeams using nonlocal strain gradient theory
title_full_unstemmed Stochastic dispersion behavior and optimal design of locally resonant metamaterial nanobeams using nonlocal strain gradient theory
title_sort Stochastic dispersion behavior and optimal design of locally resonant metamaterial nanobeams using nonlocal strain gradient theory
author_id_str_mv 5894777b8f9c6e64bde3568d68078d40
author_id_fullname_str_mv 5894777b8f9c6e64bde3568d68078d40_***_Michael Friswell
author Michael Friswell
author2 T. Chatterjee
S. El-Borgi
M. Trabelssi
Michael Friswell
format Journal article
container_title Probabilistic Engineering Mechanics
container_volume 81
container_start_page 103777
publishDate 2025
institution Swansea University
issn 0266-8920
1878-4275
doi_str_mv 10.1016/j.probengmech.2025.103777
publisher Elsevier BV
college_str Faculty of Science and Engineering
hierarchytype
hierarchy_top_id facultyofscienceandengineering
hierarchy_top_title Faculty of Science and Engineering
hierarchy_parent_id facultyofscienceandengineering
hierarchy_parent_title Faculty of Science and Engineering
department_str School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Aerospace Engineering{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Aerospace Engineering
document_store_str 1
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description 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.
published_date 2025-07-01T05:28:45Z
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