Mathematical modelling and virtual design of metamaterials for reducing noise and vibration in built-up structures
Abstract
Noise and vibration are pervasive challenges in built-up structures, impacting structural integrity, operational efficiency, and occupant well-being. These issues are particularly pronounced in urban and industrial settings, where traditional materials often struggle to deliver effective mitigation across the broad range of relevant frequencies. This paper introduces an integrated mathematical modeling and virtual design framework for the development of advanced metamaterials aimed at reducing noise and vibration in such complex structures. The approach combines finite element analysis, dynamic energy analysis, and optimization algorithms to design metamaterials with frequency-selective properties that create targeted barriers to acoustic and vibrational disturbances. The study not only develops a systematic methodology for designing these metamaterials but also validates their efficacy through comprehensive simulations and benchmarking against established solutions. The results highlight the advantages of the proposed metamaterials in terms of adaptability, efficiency, and performance robustness across various operating conditions. Sensitivity analyses and comparative evaluations further underscore the superiority of the framework in addressing frequency-dependent challenges, offering significant improvements over conventional materials. A unique aspect of this research is the inclusion of natural metamaterials (NMs) as a sustainable alternative for mitigating ground vibrations. The study reviews the potential of NMs for diverse functionalities, particularly in attenuating ground vibrations in urban environments. These findings emphasize the versatility and eco-friendliness of natural materials, providing a roadmap for their development and application in achieving clean and quiet environments. The proposed framework, therefore, bridges theoretical advancements with practical applications, paving the way for resilient and sustainable solutions to noise and vibration challenges in built-up structures.Downloads
References
N. M. Abusag, D. J. Chappell. On sparse reconstructions in near-field acoustic holography using the method of superposition. Journal of Computational Acoustics. - 2016. - Vol. 24. - No. 03. - p.1650009. DOI: https://doi.org/10.1142/S0218396X16500090
Q. Aumann, M. Miksch, G. Muller. Parametric model order reduction for acoustic metamaterials based on local thickness variations. Journal of Physics: Conference Series. - 2019 - No. 1264. - P. 1-11. DOI: https://doi.org/10.1088/1742-6596/1264/1/012014
J. Bajars, D. Chappell, N. Sondergaard, G. Tanner, Computing high-frequency wave energy distributions in two and three dimensions using discrete flow mapping. Proceedings of the 22nd International Congress on Sound and Vibration (ICSV22) - 2015.
J. Bajars, D.J. Chappell, Modelling uncertainties in phase-space boundary integral models of ray propagation, Communications in Nonlinear Science and Numerical Simulation. - 2020. - Vol. 80. - 104973. - P. 1-19. DOI: https://doi.org/10.1016/j.cnsns.2019.104973
M. Bopp, A. Albers. Vibroacoustic metamaterials as add-on solution for noise reduction in existing housing structures. In INTER-NOISE and NOISE-CON Congress and Conference Proceedings Institute of Noise Control Engineering. - 2023. - Vol. 265. - P. 4420-4430. DOI: https://doi.org/10.3397/IN_2022_0632
F. Cavaliere, S. Zlotnik, R. Sevilla, X. Larrayoz, P. Diez, Nonintrusive parametric nvh study of a vehicle body structure. Mechanics Based Design of Structures and Machines. - 2022. - Vol. 51. - P. 6557-6582. DOI: https://doi.org/10.1080/15397734.2022.2098140
G. Cerniauskas, H. Sadia, P. Alam. Machine intelligence in metamaterials design: a review. Oxford Open Materials Science. - 2024. Vol. 4. No. 1. - P. 1-30. DOI: https://doi.org/10.1093/oxfmat/itae001
W. Chai, M. Feng. Vibration control of super tall buildings subjected to wind loads. International Journal of Non-linear Mechanics. - 1997. - Vol. 32. - P. 657-668.
D. Chappell, M. Abusag. The method of superposition for near-field acoustic holography in a semi-anechoic chamber. Integral Methods in Science and Engineering: Practical Applications. - 2017. - Vol. 2. - P. 21-29. DOI: https://doi.org/10.1007/978-3-319-59387-6_3
D. Chappell, J.J. Crofts, M. Richter, G. Tanner. A direction preserving discretization for computing phase-space densities. SIAM Journal on Scientific Computing. - 2021. - Vol. 43, No. 4. - P. B884-B906. DOI: https://doi.org/10.1137/20M1352041
D. Chappell, P. Harris, D. Henwood, R. Chakrabarti. A stable boundary element method for modeling transient acoustic radiation. The Journal of the Acoustical Society of America. - 2006. - Vol. 120, No. 1. - P. 74-80. DOI: https://doi.org/10.1121/1.2202909
D.J. Chappell, N. Sondergaard, G. Tanner. Discrete flow mapping for interior acoustic modelling. Chaos: Royal Society of London Proceedings Series. - 2013. - Vol. A, No. 469. - P. 1-14. DOI: https://doi.org/10.1098/rspa.2013.0153
D.J. Chappell, G. Tanner. A boundary integral formalism for stochastic ray tracing in billiards. Chaos: An Interdisciplinary Journal of Nonlinear Science. - 2014. - Vol. 24, No. 4. DOI: https://doi.org/10.1063/1.4903064
D.J. Chappell, G. Tanner. Uncertainty quantification for phase-space boundary integral models of ray propagation. Wave Motion. - 2019. - Vol. 87. - P. 151-165. DOI: https://doi.org/10.1016/j.wavemoti.2018.08.010
J. Du, N. Olhoff. Minimization of sound radiation from vibrating bi-material structures using topology optimization. Structural and Multidisciplinary Optimization. - 2007. - Vol. 33. - P. 305-321.DOI: https://doi.org/10.1007/s00158-006-0088-9
T. Dutton, D. Chappell, D. Smith. Wave and finite element modelling of automotive joints including lightweight composites. PROCEEDINGS OF ISMA2020 AND USD2020. -- 2020.
B. Fang, A. Kelkar, S. Joshi, H. Pota. Modelling, system identification, and control of acoustic structure dynamics in 3-d enclosures. Control Engineering Practice. - 2004. - Vol. 12. - P. 989-1004.
Z. Fang, J. Zhan. Deep physical informed neural networks for metamaterial design. IEEE Access. - 2019. - Vol. 8. - P. 24506-24513. DOI: https://doi.org/10.1109/ACCESS.2019.2963375
U. Gabbert, J. Lefevre, T. Nestorovi, S. Ringwelski. Analysis and design of smart structures to control vibration and noise. International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. - 2007. - Vol. 48027. - P. 49-56.
T. Hartmann, S. Morita, G. Tanner, D.J. Chappell. High-frequency structure-and air-borne sound transmission for a tractor model using dynamical energy analysis. Wave Motion. - 2019. - Vol. 87. - P. 132-150. DOI: https://doi.org/10.1016/j.wavemoti.2018.09.012
R. Hedayati, S.P. Lakshmanan. Active acoustic metamaterial based on helmholtz resonators to absorb broadband low-frequency noise. Materials. - 2024. - Vol. 17, No. 4. - P. 962. DOI: https://doi.org/10.3390/ma17040962
M. Ichchou, A.A. Kacem. Reduced models for elastoacoustic problems with intelligent interfaces. Journal of the Acoustical Society of America. - 2008. - Vol. 123. - P. 3573-3573. DOI: https://doi.org/10.1121/1.2934653
J. Ji, Q. Luo, K. Ye. Vibration control based metamaterials and origami structures: A state-of-the-art review. Mechanical Systems and Signal Processing. - 2021. - Vol. 161. - P. 107945. DOI: https://doi.org/10.1016/j.ymssp.2021.107945
A. Keane. Passive vibration control via unusual geometries: the application of genetic algorithm optimization to structural design. Journal of Sound and Vibration. - 1995. - Vol. 185. - P. 441-453. DOI: https://doi.org/10.1006/jsvi.1995.0391
S. Khot, N.P. Yelve, R. Nair. Simulation study of active vibration control of cantilever beam by using state and output feedback control laws. ASME International Mechanical Engineering Congress and Exposition. - 2013. - Vol. 56253. - P. V04BT04A055.
S. Khot, N.P. Yelve, R. Tomar, S. Desai, S. Vittal. Active vibration control of cantilever beam by using pid based output feedback controller. Journal of Vibration and Control. - 2012. - Vol. 18. - P. 366-372. DOI: https://doi.org/10.1177/1077546311406307
R. Martin. A numerical simulation of neural fields on curved geometries. Journal of computational neuroscience. -- 2018. - Vol. 45. - P. 133-145. DOI: https://doi.org/10.1007/s10827-018-0697-5
F. Mittermeier, J. Schauer, M. Miksch, G. M?ller. Numerical investigation of the potential of tailored inclusions as noise reduction measures. Journal of Physics: Conference Series. - 2019. - Vol. 1264. DOI: https://doi.org/10.1088/1742-6596/1264/1/012013
N. Mohammed, S. Creagh, G. Tanner, D. Chappell. Tunnelling corrections to wave transmissions on shell structures. 28th Proc. Int. Conf. on Noise and Vibration Engineering ISMA. - 2018. - P. 2349-2362.
L. Nash, D. Kleckner, A. Read, V. Vitelli, A. Turner, W. Irvine. Topological mechanics of gyroscopic metamaterials. Proceedings of the National Academy of Sciences. - 2015. - Vol. 112. - P. 14495-14500. DOI: https://doi.org/10.1073/pnas.1507413112
R. Ohayon, C. Soize. Structural acoustics and vibration. The Journal of the Acoustical Society of America. - 2001. - Vol. 109. - P. 2545-2546. DOI: https://doi.org/10.1121/1.1352086
A.S. Qahtan, J. Huang, M. Amran, D.N. Qader, R. Fediuk, A.D. Wael. Seismic composite metamaterial: a review. Journal of Composites Science. - 2022. - Vol. 6, No. 11. - P. 348. DOI: https://doi.org/10.3390/jcs6110348
H. Qin, D. Yang. Vibration reduction design method of metamaterials with negative poisson's ratio. Journal of Materials Science. - 2019. - Vol. 54. - P. 14038-14054. DOI: https://doi.org/10.1007/s10853-019-03903-z
M. Richter, D. Chappell, G. Tanner. Dynamical energy analysis: high-frequency vibrational excitation of real-world structures. Proceedings of ISMA2020 International Conference on Noise and Vibration Engineering. - 2020. - P. 1711-1719.
M. Richter, D.J. Chappell. Convergence of ray-based methods using transfer operators in different bases. Forum Acusticum, Dec 2020, Lyon, France. - 2020. - P. 231-237. DOI: https://doi.org/10.48465/fa.2020.0738
J. Rowbottom, D.J. Chappell. On hybrid convolution quadrature approaches for modeling time-domain wave problems with broadband frequency content. International Journal for Numerical Methods in Engineering. - 2021. - Vol. 122. - No. 24. - P. 7581-7608. DOI: https://doi.org/10.1002/nme.6844
J. Rowbottom, D.J. Chappell. A numerical study of the convergence of two hybrid convolution quadrature schemes for broadband wave problems. In Integral Methods in Science and Engineering--Cham, C. Constanda, B. E. Bodmann, and P. J. Harris, Eds., Springer International Publishing. - 2022. - P. 291-305. DOI: https://doi.org/10.1007/978-3-031-07171-3_20
A. Saxena, C. Tsakonas, D. Chappell, C.S. Cheung, A.M.J. Edwards, H. Liang, I.C. Sage, C.V. Brown. Static and dynamic optical analysis of micro wrinkle formation on a liquid surface. Micromachines. - 2021. - Vol. 12, No. 12. - P.1583. DOI: https://doi.org/10.3390/mi12121583
J. Slipantschuk, M. Richter, D.J. Chappell, G. Tanner, W. Just, O.F. Bandtlow. Transfer operator approach to ray-tracing in circular domains. Nonlinearity. - 2020. - Vol. 33, - No. 11. - P. 5773. DOI: https://doi.org/10.1088/1361-6544/ab9dca
N. Sondergaard, D. J. Chappell. Ray and wave scattering in smoothly curved thin shell cylindrical ridges. Journal of Sound and Vibration. - 2016. - Vol. 377. - P. 155-168. DOI: https://doi.org/10.1016/j.jsv.2016.05.019
J.S. Tamber, D.J. Chappell, J.C. Poore, M.R. Tranter. Detecting delamination via nonlinear wave scattering in a bonded elastic bar. Nonlinear Dynamics. - 2024. - Vol. 112, No. 1. - P. 23-33. DOI: https://doi.org/10.1007/s11071-023-08992-9
N. Tandon. Noise-reducing designs of machines and structures. Sadhana. - 2000. - Vol. 25. - P. 331-339.
G. Tanner, D. Chappell, H.B. Hamdin, S. Giani, C. Seidel, F. Vogel. Acoustic energy distribution in multi-component structures-dynamical energy analysis versus numerically exact results. PROCEEDINGS OF ISMA2010 INCLUDING USD2010. - 2010. - P. 231-237
G. Tanner, D. Chappell, D. L{"o}ckel, N. S{o}ndergaard, F. Vogel. Dynamical energy analysis on mesh grids: A new tool for describing the vibro-acoustic response of complex mechanical structures. Wave Motion. - 2014. - Vol. 51. DOI: https://doi.org/10.1016/j.wavemoti.2014.01.004
S. Vasut, P. Bris, P. Ponizil. Mathematical model for the design of layered structures to provide vibration and impact damping. Building Acoustics. - 2001. - Vol. 8/1. - P. 25-39. DOI: https://doi.org/10.1260/1351010011501713
E. Ventsel, T. Krauthammer, E. Carrera. Thin plates and shells: theory, analysis, and applications. Appl. Mech. Rev. - 2002. - Vol. 55, No. 4. - P. B72-B73. DOI: https://doi.org/10.1201/9780203908723
D. Yang. Ship vibration and noise reduction with metamaterial structures. In Practical Design of Ships and Other Floating Structures: Proceedings of the 14th International Symposium, PRADS 2019, September 22-26, 2019, Yokohama, Japan, Springer. - 2021. - Vol. 2. No. 14. - P. 377-386. DOI: https://doi.org/10.1007/978-981-15-4672-3_24
L. Zhang, X. Sheng. A review on the research progress of mechanical meta-structures and their applications in rail transit. Intelligent Transportation Infrastructure. - 2022. - P. 1-32. DOI: https://doi.org/10.1093/iti/liac010
Copyright (c) 2024 Emmanuel Akaligwo, Anselm Oyem, Olayiwola Babanrinsa
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
The copyright holder is the author.
Authors who publish with this journal agree to the following terms:
1. Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal. (Attribution-Noncommercial-No Derivative Works licence).
2. Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
3. Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (see The Effect of Open Access).
