Theoretical Evidence For Ultrasonic Insulation Using a Fractal-Like Phononic Crystal Membranes


  •   Abdelfattah Elmadani

  •   Abdelmajid Idrissi

  •   Ramdan Braik

  •   Saad Bensallam

  •   Abella Bouaaddi

  •   Younes Achaoui

  •   Hicham Jakjoud


Phononic crystals are artificial engineered materials designed to control and manipulate waves. Unusual behaviour of prohibiting the acoustic propagation in some frequency bands (Band GAP), is a practical way to produce sound-ultrasound-proof environments with a small spatial footprint. In this work, we present a new fractal-like phononic crystal for extraordinary ultrasonic insulation. The host material is a silicon plate where the unit cell is formed by triangular slice and immersed in water. Our simulation is made between 300 kHz and 1.2 MHz and show the possibility of obtaining a wideband-gap, inferior to the one described by the mass law related to a homogeneous silicon membrane, with an attenuation reaching -70 dB, depending on the filling factor.

Keywords: Acoustic metamaterials, band-gap, Fractal structure, Phononic crystals, Sierpiński triangle, Ultrasonic insulation


Sukhovich A, Merheb B, Muralidharan K, Vasseur JO, Pennec Y, Deymier PA, et al. Experimental and theoretical evidence for subwavelength imaging in phononic crystals. Phys Rev Lett, 2009;102:1–4.

Li Y, Yu G, Liang B, Zou X, Li G, Cheng S, et al. Three-dimensional Ultrathin Planar Lenses by Acoustic Metamaterials. Sci Rep, 2015;4:6830.

Yang M, Sheng P. Sound Absorption Structures: From Porous Media to Acoustic Metamaterials. Annu Rev Mater Res, 2017;47:83–114.

Li P, Li F, Liu Y, Shu F, Wu J, Wu Y. Temperature insensitive mass sensing of mode selected phononic crystal cavity. J Micromechanics Microengineering, 2015;25:125027.

Vasseur JO, Deymier PA, Chenni B, Djafari-Rouhani B, Dobrzynski L, Prevost D. Experimental and theoretical evidence for the existence of absolute acoustic band gaps in two-dimensional solid phononic crystals. Phys Rev Lett, 2001;86:3012–5.

Hussein MI, Leamy MJ, Ruzzene M. Dynamics of Phononic Materials and Structures: Historical Origins, Recent Progress, and Future Outlook. Appl Mech Rev, 2014;66:040802.

El Madani A. Bensallam S. Idrissi M. Addouche M. Elayouch A. Khelif A. Bouaaddi A. Achaoui Y. Jakjoud H. Investigation of Ultrasonic Opacity Based on Quarter-Wave Mode Resonance Using a Two-Dimensional Silicon Phononic Crystal. Innov. Smart Cities Appl., Springer Nature; 2021;4.

El Madani A. Bensallam S. Elayouch A. Khelif A. Achaoui Y. Bouaaddi A. Jakjoud H. Ultrasonic insulation using a Helmholtz-like phononic crystal with a slight filling factor. ACM Int Conf Proceeding Ser, 2019:3–5.

Elayouch A, Addouche M, Herth E, Khelif A. Experimental evidence of ultrasonic opacity using the coupling of resonant cavities in a phononic membrane. Appl Phys Lett, 2013;103.

Yang M, Ma G, Yang Z, Sheng P. Subwavelength perfect acoustic absorption in membrane-type metamaterials: A geometric perspective. EPJ Appl Metamaterials, 2015;2.

Tang Y, Ren S, Meng H, Xin F, Huang L, Chen T, et al. Hybrid acoustic metamaterial as super absorber for broadband low-frequency sound. Sci Rep, 2017;7:1–10.

Steurer W, Sutter-Widmer D. Photonic and phononic quasicrystals. J Phys D Appl Phys, 2007;40.

Chen AL, Wang YS, Guo YF, Wang ZD. Band structures of Fibonacci phononic quasicrystals. Solid State Commun, 2008;145:103–8.

Castiñeira-Ibáñez S, Romero-García V, Sánchez-Pérez J V., Garcia-Raffi LM. Overlapping of acoustic bandgaps using fractal geometries. EPL, 2010;92:240071–3.

Oltulu O, Ozer Z, Mamedov AM, Ozbay E. Band structures of metacompsosite based phononic crystals in quasi-Sierpinski fractals. Epa - J Silic Based Compos Mater, 2022;74:57–60.

Palaz S, Ozer Z, Mamedov AM, Ozbay E. Ferroelectric based fractal phononic crystals: wave propagation and band structure. Ferroelectrics, 2020;557:85–91.

Li L, Xie YC, Wang YQ, Hu XY, Feng ZF, Cheng BY. Absolute Gap of Two-Dimensional Fractal Photonic Structure. Chinese Phys Lett, 2003;20:1767–9.

Hou B, Xie H, Wen W, Sheng P. Three-dimensional metallic fractals and their photonic crystal characteristics. Phys Rev B - Condens Matter Mater Phys, 2008;77:1–8.

Mandelbrot BB, Wheeler JA. The Fractal Geometry of Nature. 1983;51.

Monsoriu JA, Zapata-Rodríguez CJ, Silvestre E, Furlan WD. Cantor-like fractal photonic crystal waveguides. Opt Commun, 2005;252:46–51.


How to Cite
Elmadani, A., Idrissi, A., Braik, R., Bensallam, S., Bouaaddi, A., Achaoui, Y., & Jakjoud, H. (2022). Theoretical Evidence For Ultrasonic Insulation Using a Fractal-Like Phononic Crystal Membranes. European Journal of Applied Physics, 4(4), 1–5.

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