Archives of Acoustics, 46, 1, pp. 87–93, 2021
10.24425/aoa.2021.136563

Analysis of a Geometrical-Stiffening Membrane Acoustic Metamaterial with Individually Tunable Multi-Frequencies

Junjuan ZHAO
Beijing Municipal Institute of Labor Protection
China

Xianhui LI
Beijing Municipal Institute of Labor Protection
China

David THOMPSON
University of Southampton
United Kingdom

Yueyue WANG
Beijing Municipal Institute of Labor Protection
China

Wenjiang WANG
Beijing Municipal Institute of Labor Protection
China

Liying ZHU
Beijing Municipal Institute of Labor Protection
China

Yunan LIU
Beijing Municipal Institute of Labor Protection
China

To realize a structure which can be conveniently tuned to multiple and wideband frequency ranges, a geometrical-stiffening membrane acoustic metamaterial (MAM) with individually tunable multiple frequencies is presented. The MAM is realized by a stacked arrangement of two membrane-magnet elements, each of which has a membrane with a small piece of steel attached in the centre. It can be tuned individually by adjusting the position of its compact magnet. The normal incidence sound transmission loss of the MAM is investigated in detail by measurements in an impedance tube. The test sample results demonstrate that this structure can easily achieve a transmission loss with two peaks which can be shifted individually in a wide low-frequency range. A theoretical consideration is analysed, the analysis shows that the magnetic effect related to this distance leads to a nonlinear attractive force and, consequently, nonlinear geometrical stiffening in each membrane-magnet element, which allows the peaks to be shifted. A reasonable design can make the structure have a good application prospect for low-frequency noise insulation where there is a need to adjust the transmission loss according to the spectrum of the noise source.
Keywords: membrane acoustic metamaterial; nonlinear geometric stiffening; low frequency tuning; sound transmission
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References

Chen X., Xu X., Ai S., Chen H., Pei Y., Zhou X. (2014a), Active acoustic metamaterials with tunable effective mass density by gradient magnetic fields, Applied Physics Letters, 105(7): 071913, doi: 10.1063/1.4893921.

Chen Y., Huang G., Zhou X., Hu G., Sun C.T. (2014b), Analytical coupled vibroacoustic modeling of membrane-type acoustic metamaterials: Membrane model, Journal of the Acoustical Society of America, 136(3): 969–979, doi: 10.1121/1.4892870.

Cohen H., Handelman G. (1957), On the vibration of a circular membrane with added mass, Journal of the Acoustical Society of America, 29(2): 229–233, doi: 10.1121/1.1908838.

Ding C., Hao L., Zhao X. (2010), Two-dimensional acoustic metamaterial with negative modulus, Journal of Applied Physics, 108(7): 074911, doi: 10.1063/1.3493155.

Fang N. et al. (2006), Ultrasonic metamaterials with negative modulus, Nature Materials, 5(6): 452–456, doi: 10.1038/nmat1644.

Fey J., Robertson W.M. (2011), Compact acoustic bandgap material based on a subwave length collection of detuned Helmholtz resonators, Journal of Applied Physics, 109(11): 114903, doi: 10.1063/1.3595677.

Guenneau S., Movchan A., Pétursson G., Ramakrishna S.A. (2007), Acoustic metamaterials for sound focusing and confinement, New Journal of Physics, 9(11): 399, doi: 10.1088/1367-2630/9/11/399.

Kornhauser E.T., Mintzer D. (1953), On the vibration of mass-loaded membranes, Journal of the Acoustical Society of America, 25(5): 903–906, doi: 10.1121/1.1907216.

Langfeldt F., Riecken J., Gleine W., Von Estorff O. (2016), A membrane-type acoustic metamaterial with adjustable acoustic properties, Journal of Sound & Vibration, 373: 1–18, doi: 10.1016/j.jsv.2016.03.025.

Lee S.H., Park C.M., Seo Y.M., Wang Z.G., Kim C.K. (2009), Acoustic metamaterial with negative modulus, Journal of Physics: Condensed Matter, 21(17): 175704, doi: 10.1088/0953-8984/21/17/175704.

Lee S.H., Park C.M., Seo Y.M., Wang Z.G., Kim C.K. (2010), Composite acoustic medium with simultaneously negative density and modulus, Physical Review Letters, 104(5): 054301, doi: 10.1103/PhysRevLett.104.054301.

Li J., Chan C.T. (2004), Double-negative acoustic metamaterial, Physical Review E, 70: 055602, doi: 10.1103/PhysRevE.70.055602.

Liang B., Yuan B., Cheng J.C. (2009), Acoustic diode: rectification of acoustic energy flux in one-dimensional systems, Physical Review Letters, 103(10): 104301, doi: 10.1103/PhysRevLett.103.104301.

Ma G., Fan X., Sheng P., Fink, M. (2018), Shaping reverberating sound fields with an actively tunable metasurface, Proceedings of the National Academy of Sciences, 115(26): 6638–6643, doi: 10.1073/pnas.1801175115.

Mei J., Ma G., Yang M., Yang Z., Wen W., Sheng P. (2012), Dark acoustic metamaterials as super absorbers for low-frequency sound, Nature Communications, 3(27): 7561–7567, doi: 10.1038/NCOMMS1758.

Morse P.M., Ingard K.U. (1986), Theoretical Acoustics, Princeton University Press, pp. 209–213.

Tian H., Wang X., Zhou Y. (2013), Theoretical model and analytical approach for a circular membrane-ring structure of locally resonant acoustic metamaterial, Applied Physics A, 114(3): 985–990, doi: 10.1007/s00339-013-8047-y.

Wang C.Y. (2003), Vibration of an annular membrane attached to a free, rigid core, Journal of Sound and Vibration, 260(4): 776–782, doi: 10.1016/S0022-460X(02)01198-7.

Xiao S., Ma G., Li Y., Yang Z., Sheng P. (2015), Active control of membrane-type acoustic metamaterial by electric field, Applied Physics Letters, 106(9): 091904, doi: 10.1063/1.4913999.

Yang M., Ma G., Yang Z., Sheng, P. (2013), Coupled membranes with doubly negative mass density and bulk modulus, Physical Review Letters, 110(13): 134301, doi: 10.1103/PhysRevLett.110.134301.

Zhang S., Xia C., Fang, N. (2011), Broadband acoustic cloak for ultrasound waves, Physical Review Letters, 106(2): 024301, doi: 10.1103/PhysRevLett.106.024301.

Zhang Y., Wen J., Xiao Y., Wen X., Wang J. (2012), Theoretical investigation of the sound attenuation of membrane-type acoustic metamaterials, Physics Letters A, 376(17): 1489–1494, doi: 10.1016/j.physleta.2012.03.010.

Zhao J., Li X., Wang W., Wang Y., Zhu L., Liu Y. (2019), Membrane-type acoustic metamaterials with tunable frequency by a compact magnet, Journal of the Acoustical Society of America, 145(5): EL400–EL404, doi: 10.1121/1.5107431.




DOI: 10.24425/aoa.2021.136563