Abstract
Acoustic and elastic waves can be manipulated by a novel artificial metasurface, usually composed of different microstructures. In this paper, the topology optimization technique was introduced to design single-groove acoustic metasurfaces based on genetic algorithms. The mixed variables are proposed to design the layouts of grooves, and a new objective function of anomalous refraction is established. Three case studies were obtained as follows: (1) anomalous refraction, (2) beam focusing, and (3) self-accelerating beams. Compared with the original single-groove metasurface, the optimized one has less scattering in the transmitted field, and its numerical simulation results are closer to the predicted values. This research is expected to contribute highly to the field of vibration and noise isolation, elastic wave filters, and acoustic devices.
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Tang, K., Qiu, C., Ke, M., Lu, J., Ye, Y., Liu, Z.: Anomalous refraction of airborne sound through ultrathin metasurfaces. Sci. Rep. 4, 1–7 (2014)
Xie, Y., Wang, W., Chen, H., Konneker, A., Popa, B.-I., Cummer, S.A.: Wavefront modulation and subwavelength diffractive acoustics with an acoustic metasurface. Nat. Commun. 5, 1–5 (2014)
Díaz-Rubio, A., Tretyakov, S.A.: Acoustic metasurfaces for scattering-free anomalous reflection and refraction. Phys. Rev. B 96, 125409 (2017)
Lan, J., Zhang, X., Liu, X., Li, Y.: Wavefront manipulation based on transmissive acoustic metasurface with membrane-type hybrid structure. Sci. Rep. 8, 1–9 (2018)
Wong, A.M., Eleftheriades, G.V.: Perfect anomalous reflection with a bipartite Huygens’ metasurface. Phys. Rev. X 8, 011036 (2018)
Zhou, J., Zhang, X., Fang, Y.: Analytical modelling for predicting the sound field of planar acoustic metasurface. J. Appl. Phys. 123, 033106 (2018)
Li, X.-S., Wang, Y.-F., Chen, A.-L., Wang, Y.-S.: Modulation of out-of-plane reflected waves by using acoustic metasurfaces with tapered corrugated holes. Sci. Rep. 9 (2019)
Chen, A., Tang, Q., Wang, H., Zhao, S., Wang, Y.: Multifunction switching by a flat structurally tunable acoustic metasurface for transmitted waves, Science China. Phys. Mech. Astron. 63, 244611 (2020)
Li, Y., Liang, B., Tao, X., Zhu, X.-F., Zou, X.-Y., Cheng, J.-C.: Acoustic focusing by coiling up space. Appl. Phys. Lett. 101, 233508 (2012)
Tang, D., Wang, C., Zhao, Z., Wang, Y., Pu, M., Li, X., Gao, P., Luo, X.: Ultrabroadband superoscillatory lens composed by plasmonic metasurfaces for subdiffraction light focusing. Laser Photon. Rev. 9, 713–719 (2015)
Zhai, S., Chen, H., Ding, C., Shen, F., Luo, C., Zhao, X.: Manipulation of transmitted wave front using ultrathin planar acoustic metasurfaces. Appl. Phys. A 120, 1283–1289 (2015)
Tian, Y., Tan, Z., Han, X., Li, W.: Phononic crystal lens with an asymmetric scatterer. J. Phys. D Appl. Phys. 52, 025102 (2018)
Zhang, P., Li, T., Zhu, J., Zhu, X., Yang, S., Wang, Y., Yin, X., Zhang, X.: Generation of acoustic self-bending and bottle beams by phase engineering. Nat. Commun. 5, 1–9 (2014)
Chen, X., Liu, P., Hou, Z., Pei, Y.: Magnetic-control multifunctional acoustic metasurface for reflected wave manipulation at deep subwavelength scale. Sci. Rep. 7, 1–9 (2017)
Fan, S.-W., Zhao, S.-D., Chen, A.-L., Wang, Y.-F., Assouar, B., Wang, Y.-S.: Tunable broadband reflective acoustic metasurface. Phys. Rev. Appl. 11, 044038 (2019)
Zhou, J., Zhang, X., Fang, Y.: Three-dimensional acoustic characteristic study of porous metasurface. Compos. Struct. 176, 1005–1012 (2017)
Fang, Y., Zhang, X., Zhou, J.: Experiments on reflection and transmission of acoustic porous metasurface with composite structure. Compos. Struct. 185, 508–514 (2018)
Liu, Y., Liang, Z., Liu, F., Diba, O., Lamb, A., Li, J.: Source illusion devices for flexural Lamb waves using elastic metasurfaces. Phys. Rev. Lett. 119, 034301 (2017)
Fan, X.-D., Liang, B., Yang, J., Cheng, J.-C.: Illusion for Airborne sound source by a Closed Layer with subwavelength thickness. Sci. Rep. 9, 1–6 (2019)
Zhu, H., Semperlotti, F.: Anomalous refraction of acoustic guided waves in solids with geometrically tapered metasurfaces. Phys. Rev. Lett. 117, 034302 (2016)
Zhao, S.-D., Chen, A.-L., Wang, Y.-S., Zhang, C.: Continuously tunable acoustic metasurface for transmitted wavefront modulation. Phys. Rev. Appl. 10, 054066 (2018)
Zhang, J., Zhang, X., Xu, F., Ding, X., Deng, M., Hu, N., Zhang, C.: Vibration control of flexural waves in thin plates by 3D-printed metasurfaces. J. Sound Vibr. 481, 115440 (2020)
Yuan, S.-M., Chen, A.-L., Wang, Y.-S.: Switchable multifunctional fish-bone elastic metasurface for transmitted plate wave modulation. J. Sound Vibr. 470, 115168 (2020)
Cao, L., Yang, Z., Xu, Y., Chen, Z., Zhu, Y., Fan, S.-W., Donda, K., Vincent, B., Assouar, B.: Pillared elastic metasurface with constructive interference for flexural wave manipulation. Mech. Syst. Signal Process. 146, 107035 (2021)
Xu, W., Zhang, M., Ning, J., Wang, W., Yang, T.: Anomalous refraction control of mode-converted elastic wave using compact notch-structured metasurface. Mater. Res. Express 6, 065802 (2019)
Kaveh, A., Bakhshpoori, T.: Metaheuristics: Outlines, MATLAB codes and examples. Springer (2019)
Yang, H., Cao, X., Yang, F., Gao, J., Xu, S., Li, M., Chen, X., Zhao, Y., Zheng, Y., Li, S.: A programmable metasurface with dynamic polarization, scattering and focusing control. Sci. Rep. 6, 35692 (2016)
Sun, H., Gu, C., Chen, X., Li, Z., Liu, L., Xu, B., Zhou, Z.: Broadband and broad-angle polarization-independent metasurface for radar cross section reduction. Sci. Rep. 7, 40782 (2017)
Jafar-Zanjani, S., Inampudi, S., Mosallaei, H.: Adaptive genetic algorithm for optical metasurfaces design. Sci. Rep. 8, 1–16 (2018)
Li, H., Wang, G., Cai, T., Hou, H., Guo, W.: Wideband transparent beam-forming metadevice with amplitude-and phase-controlled metasurface. Phys. Rev. Appl. 11, 014043 (2019)
Fan, Y., Xu, Y., Qiu, M., Jin, W., Zhang, L., Lam, E.Y., Tsai, D.P., Lei, D.: Phase-controlled metasurface design via optimized genetic algorithm. Nanophotonics 1, 3931–3939 (2020)
Han, J., Cao, X., Gao, J., Yu, H., Zhang, Z., Li, S.: A coding optimized polarization conversion metasurface in broadband and wide-angle. Int. J. RF Microw. Comput. Aid. Eng. 30, e22061 (2020)
Zhu, R., Qiu, T., Wang, J., Sui, S., Li, Y., Feng, M., Ma, H., Qu, S.: Multiplexing the aperture of a metasurface: inverse design via deep-learning-forward genetic algorithm. J. Phys. D Appl. Phys. 53, 455002 (2020)
Li, W., Meng, F., Huang, X.: Coding metalens with helical-structured units for acoustic focusing and splitting. Appl. Phys. Lett. 117, 021901 (2020)
Sun, H., Wang, S., Huang, S., Peng, L., Wang, Q., Zhao, W., Zou, J.: 3D focusing acoustic lens optimization method using multi-factor and multi-level orthogonal test designing theory. Appl. Acoust. 170, 107538 (2020)
Rong, J., Ye, W.: Multifunctional elastic metasurface design with topology optimization. Acta Mater. 185, 382–399 (2020)
Koohestani, K.: Form-finding of tensegrity structures via genetic algorithm. Int. J. Solids Struct. 49, 739–747 (2012)
Chen, Y., Yan, J., Feng, J., Sareh, P.: Particle swarm optimization-based metaheuristic design generation of non-trivial flat-foldable origami tessellations with degree-4 vertices. J. Mech. Design 143, 011703 (2021)
Chen, Y., Fan, L., Bai, Y., Feng, J., Sareh, P.: Assigning mountain-valley fold lines of flat-foldable origami patterns based on graph theory and mixed-integer linear programming. Comput. Struct. 239, 106328 (2020)
Chen, Y., Feng, J., Wu, Y.: Novel form-finding of tensegrity structures using ant colony systems. (2012)
Yu, N., Genevet, P., Kats, M.A., Aieta, F., Tetienne, J.-P., Capasso, F., Gaburro, Z.: Light propagation with phase discontinuities: generalized laws of reflection and refraction. Science 334, 333–337 (2011)
Xu, W., Zhang, M., Lin, Z., Liu, C., Qi, W., Wang, W.: Anomalous refraction manipulation of Lamb waves using single-groove metasurfaces. Phys. Scr. 94, 105807 (2019)
Li, S., Xu, J., Tang, J.: Tunable modulation of refracted lamb wave front facilitated by adaptive elastic metasurfaces. Appl. Phys. Lett. 112, 021903 (2018)
Li, Y., Liang, B., Gu, Z.-M., Zou, X.-Y., Cheng, J.-C.: Reflected wavefront manipulation based on ultrathin planar acoustic metasurfaces. Sci. Rep. 3, 2546 (2013)
Acknowledgements
This work is supported by the National Natural Science Foundation of China (No. 11502149,11302135), Natural Science Foundation of Liaoning Province (Nos. 2019-ZD-0229, 2019-ZD-0228 and 2019-ZD-0297), Scientific Research Fund of Liaoning Provincial Education Department (No. JYT19056), Natural Science Foundation of Suqian City (No. K202124), Scientific Research Foundation of Suqian University. The financial contributions are gratefully acknowledged.
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Funding was provided by Natural Science Foundation of Liaoning Province, 2019-ZD-0229, Weikai Xu
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We declare that we have no financial and personal relationships with other people or organizations that can inappropriately influence our work, and there is no professional or other personal interest of any nature or kind in any product, service, and/or company that could be construed as influencing the position presented in, or the review of, the manuscript entitled “Topology Optimization of Single-groove Acoustic Metasurfaces Using Genetic Algorithms.”
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Lin, Z., Wang, W., Xu, W. et al. Topology optimization of single-groove acoustic metasurfaces using genetic algorithms. Arch Appl Mech 92, 961–969 (2022). https://doi.org/10.1007/s00419-021-02084-z
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DOI: https://doi.org/10.1007/s00419-021-02084-z