Sensitivity analysis of analytically—corrected acoustic metamaterials into the spacetime domain

Sensitivity analysis of analytically—corrected acoustic metamaterials into the spacetime domain

Giada Colombo

Abstract. The present work is focused on the sensitivity analysis of analytically–corrected acoustic metamaterials with respect to the variation of relevant parameters for aeronautical applications. The performance decay of acoustic metamaterials designed in static conditions when operating in a moving flow can be mitigated using a design process involving coordinate transformations capable of recasting the convective wave equation in the form of the static D’Alembertian. To this aim, a spacetime reformulation of the problem is needed in order to ensure the formal invariance of equations under the action of spacetime coordinate transformations. The considered test case sees a circumferential domain occupied by a metafluid embedded by a conventional medium characterized by a uniform background flow and within which a monopole source is located. All the numerical simulations are done in the frequency domain using the commercial finite element method solver. A parametric study is conducted to analyze the influence of the acoustic source position with respect to the background flow and the variation of the intensity of the latter.

Keywords
Metacontinua, Spacetime, Aeroacoustic, Parametric Study

Published online 9/1/2023, 7 pages
Copyright © 2023 by the author(s)
Published under license by Materials Research Forum LLC., Millersville PA, USA

Citation: Giada Colombo, Sensitivity analysis of analytically—corrected acoustic metamaterials into the spacetime domain, Materials Research Proceedings, Vol. 33, pp 362-368, 2023

DOI: https://doi.org/10.21741/9781644902677-53

The article was published as article 53 of the book Aerospace Science and Engineering

Content from this work may be used under the terms of the Creative Commons Attribution 3.0 license. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.

References
[1] Veselago, V. G., “The Electrodynamics of Substances with Simultaneously Negative Values of ε and μ,” Physics-Uspekhi, Vol. 10, 1968, pp. 509–514. https://doi.org/10.1070/PU1968v010n04ABEH003699
[2] Pendry, J. B., “Negative Refraction Makes Perfect Lens,” The American Physical Society, Vol. 85, No. 18, 2000. https://doi.org/10.1103/PhysRevLett.85.3966
[3] Smith, D. R., “Composite medium with simultaneously negative permeability and permittivity,” The American Physical Society, Vol. 84, No. 18, 1999. https://doi.org/10.1103/PhysRevLett.84.4184
[4] Pendry, J. B., Schurig, D., and Smith, D. R., “Controlling Electromagnetic Fields,” Science, Vol. 312, 2006, pp. 1780–1782. https://doi.org/10.1126/science.1125907
[5] Leonhardt, U., “Optical conformal mapping,” Science, Vol. 23, 2006. https://doi.org/10.1126/science.1126493
[6] Leonhardt, U., and Philbin, T. G., “General relativity in electrical engineering,” New Journal of Physics, Vol. 8, 2006. https://doi.org/10.1088/1367-2630/8/10/247
[7] Norris, A., “Acoustic cloaking theory.” Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 464, 2008, pp. 2411–2434. https://doi.org/10.1098/rspa.2008.0076
[8] Norris, A., “Acoustic metafluids.” The Journal of the Acoustical Society of America, Vol. 125, 2009, pp. 839–849. https://doi.org/10.1121/1.3050288
[9] Iemma, U., “Theoretical and Numerical Modeling of Acoustic Metamaterials for Aeroacoustic Applications,” Aerospace, Vol. 3, No. 2, 2016. https://doi.org/10.3390/aerospace3020015
[10] Iemma, U., and Palma, G., “On the Use of the Analogue Transformation Acoustics in Aeroacoustics,” Mathematical Problems in Engineering, Vol. vol. 2017, 2017, p. 16 pages. https://doi.org/https://doi.org/10.1155/2017/8981731
[11] Iemma, U., and Palma, G., “Convective correction of metafluid devices based on Taylor transformation,” Journal of Sound and Vibration, Vol. 443, 2018, pp. 238–252. https://doi.org/10.1016/j.jsv.2018.11.047
[12] Iemma, U., and Palma, G., “Design of metacontinua in the aeroacustic spacetime”, Scientific Reports, Vol. 10, 2020. https://doi.org/10.1038/s41598-020-74304-5
[13] Colombo, G., Palma, G., and Iemma, U., “Validation of analytic convective corrections for metacontinua in the aeroacoustic spacetime,” Proceedings of the 28th International Congress on Sound and Vibration, ICSV, 2022
[14] “COMSOL Multiphysics® v. 5.4”, 2018. URL https://www.comsol.com