Enhancement of sound absorber by multi-area Helmholtz resonators array based on Fibonacci sequence

Document Type : Research Paper

Author

Corresponding Author, Associate Professor, Department of Acoustics and Sound Engineering, IRIB University, P.O. Box 1986916511, Tehran, Iran

Abstract

This paper presents an innovative idea to the noise control problem for broader absorption bandwidth at low frequencies. For this aim, Helmholtz resonator array (HRA) designed based on Fibonacci sequence, which is addressed “Fibonacci based-HRA”. First, to validate the simulations which were performed through finite element method (FEM) as a numerical method in COMSOL Multi-physics software (Version 5.2), the results have been compared with experimental results which obtained by other researchers for two cases: (1) one unit resonator, and (2) four resonators array block with equal size. Second, to examine the performance of sound absorption of Fibonacci based-HRA, the results obtained for HRA with equal sizes of the 4, 6, 8 and 10 component resonators, compared with those obtained for Fibonacci based-HRA with the same number of the component resonators and the same overall dimensions of HRA block. The comparison showed that Fibonacci based-HRA approach is a good candidate for broad-band low frequency noise control.

Keywords

Main Subjects

References

 
[1] Park, J.H., Minn, K.S., Lee, H.R., Yang, S.H., Yu, Ch.B., Pak, S.Y., Oh, Ch.S., Song, Y.S., Kang, Y.J., and Youn, J.R., “Cell Openness Manipulation of Low Density Polyurethane Foam for Efficient Sound Absorption”, J. Sound Vib. Vol. 406, pp. 224-236, (2017).
 
[2] Gwon, J.G., Kim, S.K., and Kim, J.H., “Development of Cell Morphologies in Manufacturing Flexible Polyurethane Urea Foams as Sound Absorption Materials”, J. Porous Mater, Vol. 23, pp. 465-473, (2016).
 
[3] Basirjafari, S., Malekfar, R., and Khadem, S.E., “Low Loading of Carbon Nanotubes to Enhance Acoustical Properties of Poly(ether)Urethane Foams”, J. Appl. Phys. Vol. 112, pp. 104312-1 8, (2012).
 
[4] Kim, B.S., and Park, J., “Double Resonant Porous Structure Backed by Air Cavity for Low Frequency Sound Absorption Improvement”, Compos. Struct, Vol. 1, pp. 6-27, (2017).
 
[5] Zhao, X.D., and Fan, X.Q., “Enhancing Low Frequency Sound Absorption of Microperforated Panel Absorbers by using Mechanical Impedance Plates”, Appl. Acoust, Vol. 88, pp. 123-138, (2015).
 
[6] Selamet, A., and Lee, I., “Helmholtz Resonator with Extended Neck”, J. Acoust. Soc. Am. Vol. 113, pp. 1975-1985, (2003).
 
[7] Sakagami, K., Nagayama, Y., Morimoto, M., and Yairi, M., “Pilot Study on Wideband Sound Absorber Obtained by Combination of Two Different Microperforated (MPP) Absorbers”, Acoustic. Sci. Tech. Vol. 30, pp. 154-156, (2009).
 
[8] Broghany, M., Basirjafari, S., and Saffar, S., “Optimization of Flat Multi-layer Sound Absorber by using Multi-objective Genetic Algorithm for Application in Anechoic Chamber”, Modares Mech. Eng. Vol. 16, No. 2, pp. 215-222, (2016).
 
[9] Broghany, M., Saffar, S., and Basirjafari, S., “Increasing of the Frequency Band of Sound Absorption for Flat Multi-layered Absorbers Consist of Porous Material, Perforated Panel and Air-gap”, Amirkabir Journal of Mechanical Engineering, Vol. 50, pp. 219-230, (2018).
 
[10] Zou, J., Shen, Y., Yang, J., and Qiu, X., “A Note on the Prediction Method of Reverberation Absorption Coefficient of Double Layer Micro-perforated Membrane”, Appl. Acoust. Vol. 67, pp. 106-111, (2006).
 
[11] Ruiz, H., Cobo, P., and Jacobsen, F., “Optimization of Multiple-layer Microperforated Panels by Simulated Annealing”, Appl. Acoust. Vol. 72, pp. 772-776, (2011).
 
[12] Falsafi, I., and Ohadi, A., “Design Guide of Single Layer Micro Perforated Panel Absorber with Uniform Air Gap”, Appl. Acoust. Vol. 126, pp. 48-57, (2017).
 
[13] Yairi, M., Sakagami, K., Morimoto, M., and Minemura, A., “Acoustical Properties of Microperforated Panel Absorbers with Various Configurations of the Back Cavity”, Acoust. Sci. & Tech., Vol. 26, pp. 100-110, (2005).
[14] Toyoda, M., and Takahashi, D., “Sound Transmission through a Microperforated-panel Structure with Subdivided Air Cavities”, J. Acoust. Soc. Am. Vol. 124, pp. 3594-3603, (2008).
 
[15] Liu, J., and Herrin, D.W., “Enhancing Micro-perforated Panel Attenuation by Partitioning the Adjoining Cavity”, App. Acoust. Vol. 71, pp. 120-127, (2010).
 
[16] Huang, S., Li, Sh., Wang, X., and Mao, D., “Micro-perforated Absorbers with Incompletely Partitioned Cavities”, Appl. Acoust. Vol. 126, pp. 114-119, (2017).
 
[17] Lu, Y.D., Tang, H., Wang, Q., Tian, J., Qu, Y., and Qiu, B., “The Perforated Panel Resonator with Flexible Tube Bundles and its Applications”, J. Acoust. Soc. Am. Vol. 123, pp. 2983-2999, (2008).
 
[18] Zhang, Q., Lu, Y.D., Yang, J., Wei, X.W., and Wang Y.Q., “Experiment Study on the Sound Absorption Characteristic of Perforated Panel with Ladder Tube Bundles”, Noise Vib. Control. Vol. 2, pp.  253-256, (2009).
 
[19] Li, D., Chang, D., and Liu, B., “Enhancing the Low Frequency Sound Absorption of a Perforated Panel by Parallel-arranged Extended Tubes”, Appl. Acoust. Vol. 102, pp. 126-132, (2016).
 
[20] Wang, Ch., and Huang, L., “On the Acoustic Properties of Parallel Arrangement of Multiple Micro-perforated Panel Absorbers with Different Cavity Depths”, J. Acoust. Soc. Am. Vol. 130, pp. 208-218, (2011).
 
[21] Wang, C.Q., Huang, L.X., and Zhang, Y.M., “Oblique Incidence Sound Absorption of Parallel Arrangement of Multiple Micro-perforated Panels in a Periodic Pattern”, J. Sound Vib. Vol. 333, pp. 6828-6842, (2014).
 
[22] Guo, W., and Min, H., “A Compound Micro-perforated Panel Sound Absorber with Partitioned Cavities of Different Depths”, Energy Procedia, Vol. 78, pp. 1617-1622, (2015).
 
[23] Tang, Y., Ren, Sh., Meng, H., Xin, F., Huang, L., Chen, T., Zhang, Ch., and Lu, T.J., “Hybrid Acoustic Metamaterial as Super Absorber for Broadband Low-frequency Sound”, Sci. Rep. Vol. 7,  43340-1 11, (2017).
 
[24] Li, D., and Cheng, L., “Acoustically Coupled Model of an Enclosure and a Helmholtz Resonator Array”, J. Sound Vib. Vol. 305, pp. 272-288, (2007).
 
[25] Park, S.H., “Acoustic Properties of Micro-perforated Panel Absorbers Backed by Helmholtz Resonators for the Improvement of Low-frequency Sound Absorption”, J. Sound Vib. Vol. 332, pp.  4895-4811, (2013).
 
[26] Seo, S.H., and Kim, Y.H., “Silencer Design by using Array Resonators for Low-frequency Band Noise Reduction”, J. Acoust. Soc. Am. Vol. 118, pp. 2332-2338, (2005).
 
[27] http://www.mcs.zinn-x.com/images/fibonacci-nature-nautilus4.jpg.
 
[28] http://maths.survey.ac.uk/hosted-sites/R.Knott/Fibonacci Numbers in Real LSife (date of access 24.01.2017).
 
[29] http://pass.maths.org.uk/issue3/fiibonacci
 
[30] http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fib.html
 
[31] http://evolutionoftruth.com/goldensection/goldsect.htm
 
[32] Hogat, V.E., “Fibonacci and Lucas Numbers”, Palo Alto, C: Houghton-Mifflin, (1969).
 
[33] Horadam, A.F., “A Generalized Fibonacci Sequence”, Math Mag, Vol. 68, pp. 455-459,  (1961),
 
[34] Shanon, A.G., and Horadam, A.F., “Generalized Fibonacci Triples”, Amer Math Monthly, Vol. 80, pp. 187-190, (1973).
 
[35] Spinadel, V.W., “The Family of Metallic Means”, Vis Math, Vol. 1, pp. 4-8, (1999).
 
[36] Br´od, D., Piejko, K., and Wloch, I., “Distance Fibonacci Numbers, Distance Lucas Numbers and their Applications”, Ars Combinatoria, CXII, pp. 397-410, (2013).
 
[37] Falcon, S., and Plaza, A., “On the Fibonacci k–numbers”, Solitons & Fractals, Vol. 32, pp. 1615-1624, (2007).
 
[38] Falcon, S., and Plaza, A., “The k–Fibonacci Sequence and the Pascal 2–triangle”, Chaos, Solit. & Fract, Vol. 33, pp. 38-49, (2007).
 
[39] Beranek L. L., and VeI. L. r., “Noise and Vibration Control Engineering-principles and Applications”, Noise and Vibration Control Engineering-Principles and Applications, John Wiley & Sons, Inc.,Vol. 1, pp. 814-819, (1992).
 
[40] Kim, S.R., Kim, M.S., Kim, Y.H., and Kim, Y.W., “Absorptive Characteristics of Resonator Panel for Low Frequency Noise Control,and its Applications”, The 32nd International Congress and Exposition on Noise Control Engineering, Jeju International Convention Center, Seogwipo, Korea, pp. 100-110, August 25-28, (2003),
Iranian Journal of Mechanical Engineering Transactions of the ISME
Volume 22, Issue 1 - Serial Number 36
Winter and Spring
March 2021
Pages 54-73

Files

Share

How to cite

Statistics