A new Helmholtz type sonic crystal for wide-band sound attenuation
Abstract
In this paper, a Helmholtz shape sonic crystal is proposed for bandgap realization and sound attenuation. Using Bloch’s theory, bandgap properties of the sonic crystal are investigated for the primitive design of the unit-cell. A geometrical parametric study is implemented for the unit-cell to present its potential in creating bandgaps over the low-frequency range, and an optimization is applied to find its best design according to the low-frequency objective function. A frequency analysis and experimental tests are used to verify the calculated bandgaps from Bloch’s theory and to confirm the sound attenuation ability of the proposed design. It is shown that the present design not only creates wide bandgap frequencies in the low-frequency range but also, due to the Helmholtz shape of the unit-cell, provides significant sound attenuation.
Copyright (c) 2025 Author(s)

This work is licensed under a Creative Commons Attribution 4.0 International License.
References
[1]Clark C, Stansfeld SA. The Effect of Transportation Noise on Health and Cognitive Development: A Review of Recent Evidence. International Journal of Comparative Psychology. 2007; 20(2). doi: 10.46867/ijcp.2007.20.02.10
[2]Singh N, Davar SC. Noise Pollution-Sources, Effects and Control. Journal of Human Ecology. 2004; 16(3): 181–187. doi: 10.1080/09709274.2004.11905735
[3]Mahesh K, Mini RS. Theoretical investigation on the acoustic performance of Helmholtz resonator integrated microperforated panel absorber. Applied Acoustics. 2021; 178: 108012. doi: 10.1016/j.apacoust.2021.108012
[4]Radosz J. Acoustic performance of noise barrier based on sonic crystals with resonant elements. Applied Acoustics. 2019; 155: 492–499. doi: 10.1016/j.apacoust.2019.06.003
[5]Elford DP, Chalmers L, Kusmartsev FV, Swallowe GM. Matryoshka locally resonant sonic crystal. The Journal of the Acoustical Society of America. 2011; 130(5): 2746–2755. doi: 10.1121/1.3643818
[6]Sánchez-Pérez JV, Caballero D, Mártinez-Sala R, et al. Sound Attenuation by a Two-Dimensional Array of Rigid Cylinders. Physical Review Letters. 1998; 80(24): 5325–5328. doi: 10.1103/physrevlett.80.5325
[7]Ho KM, Cheng CK, Yang Z, et al. Broadband locally resonant sonic shields. Applied Physics Letters. 2003; 83(26): 5566–5568. doi: 10.1063/1.1637152
[8]Martínez-Sala R, Rubio C, García-Raffi LM, et al. Control of noise by trees arranged like sonic crystals. Journal of Sound and Vibration. 2006; 291(1–2): 100–106. doi: 10.1016/j.jsv.2005.05.030
[9]Caballero D, Sánchez-Dehesa J, Rubio C, et al. Large two-dimensional sonic band gaps. Physical Review E. 1999; 60(6): R6316.
[10]Peiró-Torres MP, Redondo J, Bravo JM, et al. Open Noise Barriers Based on Sonic Crystals. Advances in Noise Control in Transport Infrastructures. Transportation Research Procedia. 2016; 18: 392–398. doi: 10.1016/j.trpro.2016.12.051
[11]Alagoz S. An analysis of the spatio-spectral acoustic filtering effect of sonic crystals. Chinese Journal of Physics. 2016; 54(5): 788–794. doi: 10.1016/j.cjph.2016.08.003
[12]Sánchez-Dehesa J, Torrent D. A gradient index sonic lens based on acoustic metamaterials. The Journal of the Acoustical Society of America. 2007; 122: 2966–2966. doi: 10.1121/1.2942578
[13]Torrent D, Sánchez-Dehesa J. Acoustic metamaterials for new two-dimensional sonic devices. New Journal of Physics. 2007; 9(9): 323–323. doi: 10.1088/1367-2630/9/9/323
[14]Bühling B, Maack S, Strangfeld C. Using sonic crystals to separate the acoustic from the flow field of a fluidic transducer. Applied Acoustics. 2022; 189: 108608. doi: 10.1016/j.apacoust.2021.108608
[15]Mohapatra K, Jena DP. Insertion loss of sonic crystal made with multi resonant shells. Applied Acoustics. 2021; 171: 107676. doi: 10.1016/j.apacoust.2020.107676
[16]Chen Y, An S, Lan Z, et al. Multiband acoustic helical interface states in inverse-designed sonic crystals with glide symmetry. Composite Structures. 2024; 335: 117994. doi: 10.1016/j.compstruct.2024.117994
[17]Gupta A, Lim KM, Chew CH. Design of radial sonic crystal for sound attenuation from divergent sound source. Wave Motion. 2015; 55: 1–9. doi: 10.1016/j.wavemoti.2015.01.002
[18]Tajsham A, Younesian D, Goodini J, Hosseinkhani A. A new polyhedral sonic crystal for broadband sound barriers: Optimization and experimental study. Applied Acoustics. 2024; 218: 109881. doi: 10.1016/j.apacoust.2024.109881
[19]Shakouri A, Xu F, Fan Z. Broadband acoustic energy confinement in hierarchical sonic crystals composed of rotated square inclusions. Applied Physics Letters. 2017; 111(5). doi: 10.1063/1.4985230
[20]spinosa V, Sánchez-Morcillo VJ, Staliunas K, et al. Subdiffractive propagation of ultrasound in sonic crystals. Physical Review B. 2007; 76(14). doi: 10.1103/physrevb.76.140302
[21]Ke M, Liu Z, Qiu C, et al. Negative-refraction imaging with two-dimensional phononic crystals. Physical Review B. 2005; 72(6). doi: 10.1103/physrevb.72.064306
[22]Zheng LY, Wu Y, Ni X, et al. Acoustic cloaking by a near-zero-index phononic crystal. Applied Physics Letters. 2014; 104(16). doi: 10.1063/1.4873354
[23]Chalmers L, Elford DP, Kusmartsev FV, Swallowe GM. Acoustic band gap formation in two-dimensional locally resonant sonic crystals comprised of Helmholtz resonators. International Journal of Modern Physics B. 2009; 23: 4234–4243. doi: 10.1142/s0217979209063390
[24]Lee HM, Lim KM, Lee HP. Environmental and sound divergence effects on the performance of rectangular sonic crystals with Helmholtz resonators. Journal of Vibration and Control. 2017; 24(12): 2483–2493. doi: 10.1177/1077546316688422
[25]Chen Y, Huang X, Sun G, et al. Maximizing spatial decay of evanescent waves in phononic crystals by topology optimization. Computers & Structures. 2017; 182: 430–447. doi: 10.1016/j.compstruc.2017.01.001
[26]Jia Z, Yan Y, Bao Y, et al. Maximizing attenuation of sound waves preserving air permeability in sonic crystals via topology optimization. Applied Acoustics. 2025; 228: 110348. doi: 10.1016/j.apacoust.2024.110348
[27]Lee HM, Hua Y, Xie J, Lee HP. Parametric Optimization of Local Resonant Sonic Crystals Window on Noise Attenuation by Using Taguchi Method and ANOVA Analysis. Crystals. 2022; 12(2): 160. doi: 10.3390/cryst12020160
[28]Dong HW, Zhao SD, Zhu R, et al. Customizing acoustic dirac cones and topological insulators in square lattices by topology optimization. Journal of Sound and Vibration. 2021; 493: 115687. doi: 10.1016/j.jsv.2020.115687
[29]Redondo J, Ramírez-Solana D, Picó R. Increasing the Insertion Loss of Sonic Crystal Noise Barriers with Helmholtz Resonators. Applied Sciences. 2023; 13(6): 3662. doi: 10.3390/app13063662
[30]Li JB, Wang YS, Zhang C. Tuning of Acoustic Bandgaps in Phononic Crystals With Helmholtz Resonators. Journal of Vibration and Acoustics. 2013; 135(3). doi: 10.1115/1.4023812
[31]Han DH, Zhao JB, Zhang GJ, Yao H. Study on low-frequency band gap characteristics of a new Helmholtz type phononic crystal. Symmetry. 2021; 13(8): 1379. doi: 10.3390/sym13081379
[32]Wu LY, Chen LW. Wave propagation in a 2D sonic crystal with a Helmholtz resonant defect. Journal of Physics D: Applied Physics. 2010; 43(5): 055401. doi: 10.1088/0022-3727/43/5/055401
[33]Yang A, Li P, Wen Y, et al. Enhanced Acoustic Energy Harvesting Using Coupled Resonance Structure of Sonic Crystal and Helmholtz Resonator. Applied Physics Express. 2013; 6(12): 127101. doi: 10.7567/apex.6.127101
[34]Tamaki H, Kita H, Kobayashi S. Multi-objective optimization by genetic algorithms: A review. In: Proceedings of the IEEE Conference on Evolutionary Computation; 20–22 May 1996; Nagoya, Japan. pp. 517–522.
[35]Conn AR, Gould N, Toint P. A Globally Convergent Augmented Lagrangian Barrier Algorithm for Optimization with General Inequality Constraints and Simple Bounds. Mathematics of Computation. 1997; 66(217): 261–288.
[36]Panahi E, Hosseinkhani A, Frangi A, et al. A novel low-frequency multi-bandgaps metaplate: Genetic algorithm based optimization and experimental validation. Mechanical Systems and Signal Processing. 2022; 181: 109495. doi: 10.1016/j.ymssp.2022.109495
[37]Weile DS, Michielssen E. Genetic algorithm optimization applied to electromagnetics: A review. IEEE Transactions on Antennas and Propagation. 1997; 45(3): 343–353. doi: 10.1109/8.558650



