A Parametric Analysis on the Sound Absorbing Performance of the Locally Resonant Sonic Material Using a Mass-Damper-Spring Model
American Journal of Physics and Applications
Volume 4, Issue 5, September 2016, Pages: 124-133
Received: Jul. 11, 2016;
Accepted: Jul. 20, 2016;
Published: Aug. 3, 2016
Views 3674 Downloads 151
Bo Yuan, Department of Machinery and Electrical Engineering, Logistical Engineering University, Chongqing, China
Min Jiang, Department of Machinery and Electrical Engineering, Logistical Engineering University, Chongqing, China
Miao He, Department of Military Engineering Management, Logistical Engineering University, Chongqing, China
Shuai Tang, Department of Machinery and Electrical Engineering, Logistical Engineering University, Chongqing, China
Li Zhang, Department of Machinery and Electrical Engineering, Logistical Engineering University, Chongqing, China
Minglin Tu, Department of Machinery and Electrical Engineering, Logistical Engineering University, Chongqing, China
The locally resonant sonic material (LRSM) is a kind of structural composite. Such composite typically consists of an elastic matrix periodically embedded with metallic spheres, which are coated with soft rubber. Owing to its capability of controlling the low frequency sound, the LRSM has a promising prospect in the application of underwater acoustic materials. This paper proposes a mass-damper-spring model to explain the sound absorbing mechanism of the LRSM, and derives analytical formulae to evaluate the absorbing performance. After reasonable simplification, the analytical formulae can intuitively illustrate the relationship between the absorbing performance and the parameters of the LRSM. The correctness of the physical model was verified by comparing the analytical evaluation with the numerical result calculated by the layer-multiple-scattering method. The result shows that the sound absorption of the LRSM is induced by the energy dissipation of the damped local resonator subjected to excitations. The influence of the parameters on the absorbing performance of the LRSM is analysed systematically. It is shown that a resonator with a heavier core and a stiffer coat can produce a better sound absorbing performance.
A Parametric Analysis on the Sound Absorbing Performance of the Locally Resonant Sonic Material Using a Mass-Damper-Spring Model, American Journal of Physics and Applications.
Vol. 4, No. 5,
2016, pp. 124-133.
X. Hu, C. T. Chan, J. Zi, Two-dimensional sonic crystals with Helmholtz resonators, Physical Review E 71 (2005) 055601.
N. Fang, D. Xi, J. Xu, M. Ambati, W. Strituravanich, C. Sun, X. Zhang, Ultrasonic metamaterials with negative modulus, Nature Materials 5 (2006) 452-456.
Y. Cheng, J. Y. Xu, X. J. Liu, One-dimensional structured ultrasonic metamaterials with simultaneously negative dynamic density and modulus, Physical Review B 77 (2008) 045134.
Z. Liu, X. Zhang, Y. Mao, Y. Y. Zhu, Z. Yang, C. T. Chan, P. Sheng, Locally resonant sonic materials, Science 289 (2000) 1734-1736.
Z. Liu, C. T. Chan, P. Sheng, Three-component elastic wave band-gap material, Physical Review B 65 (2002) 165116.
P. Sheng, X. X. Zhang, Z. Liu, C. T. Chan, Locally resonant sonic materials, Physica B 338 (2003) 201-205.
H. Zhao, Y. Liu, G. Wang, J. Wen, D. Yu, X. Han, X. Wen, Resonance modes and gap formation in a two-dimensional solid phononic crystal, Physical Review B 72 (2005) 012301.
G. Wang, X. Wen, J. Wen, L. Shao, Y. Liu, Two-dimensional locally resonant phononic crystals with binary structures, Physical Review Letter 93 (2004) 154302.
G. Wang, L. Shao, Y. Liu, J. Wen, Accurate evaluation of lowest band gaps in ternary locally resonant phononic crystals, Chinese Physics 15 (2006) 1843-1848.
R. Sainidou, B. Djafari-Rouhani, Y. Pennec, J. O. Vasseur, Locally resonant phononic crystals made of hollow spheres or cylinders, Physical Review B 73 (2006) 024302.
Y. W. Gu, X. D. Luo, M. H. R, Optimization of the local resonant sonic material by tuning the shape of the resonator, Journal of Physics D: Applied Physics 41 (2008) 205402.
K. M. Ho, C. K. Cheng, Z. Yang, X. X. Zhang, P. Sheng, Broadband locally resonant sonic shields, Applied Physics Letters 83 (2003) 5566-5568.
M. Hirsekorn, P. P. Delsanto, N. K. Batra, P. Matic, Modelling and simulation of acoustic wave propagation in locally resonant sonic materials, Ultrasonics 42 (2004) 231-235.
M. Hirsekorn, Small-size sonic crystals with strong attenuation bands in the audible frequency range, Applied Physics Letters 84 (2004) 3364-3366.
C. Goffaux, J. Sanchez-Dehesa, A. L. Yeyati, P. Lambin, A. Khelif, J. O. Vasseur, B. Djafari-Rouhani, Evidence of Fano-like interference phenomena in locally resonant materials, Physical Review Letter 88 (2002) 225502.
H. Zhao, Y. Liu, J. Wen, D. Yu, G. Wang, X. Wen, Sound absorption of locally resonant sonic materials, Chinese Physics Letters 23 (2006) 2132-2134.
H. Zhao, Y. Liu, J. Wen, D. Yu, X. Wen, Tri-component phononic crystals for underwater anechoic coatings, Physics Letters A 367 (2007) 224-232.
H. Zhao, J. Wen, D. Yu, X. Wen, Low-frequency acoustic absorption of localized resonances: Experiment and theory, Journal of Applied Physics 107 (2010) 023519.
J. Wen, H. Zhao, L. Lv, B. Yuan, G. Wang, X. Wen, Effects of locally resonant modes on underwater sound absorption in viscoelastic materials, Journal of the Acoustical Society of America 130 (2011) 1201-1208.
H. Meng, J. Wen, H. Zhao, X. Wen, Optimization of locally resonant acoustic metamaterials on underwater sound absorption characteristics, Journal of Sound and Vibration 331 (2012) 4406-4416.
H. Jiang, Y. Wang, M. Zhang, Y. Hu, D. Lan, Y. Zhang, B. Wei, Locally resonant phononic woodpile: A wide band anomalous underwater acoustic absorbing material, Applied Physics Letters 95 (2009) 104101.
Z. Liu, C. T. Chan, P. Sheng, Analytic model of phononic crystals with local resonances, Physical Review B 71 (2005) 014103.
P. Sheng, J. Mei, Z. Liu, W. Wen, Dynamic mass density and acoustic metamaterials, Physica B 394 (2007) 256-261.
S. H. Lee, C. M. Park, Y. M. Seo, Z. G. Wang, C. K. Kim, Acoustic metamaterial with negative modulus, Journal of Physics: Condensed Matter 21 (2009) 175704.
S. H. Lee, C. M. Park, Y. M. Seo, Z. G. Wang, C. K. Kim, Acoustic metamaterial with negative density, Physics Letters A 373 (2009) 4464-4469.
S. Guenneau, A. Movchan, PéturssonG, S. A. Ramakrishna, Acoustic metamaterials for sound focusing and confinement, New Journal of Physics 9 (2007) 399.
J. Li, Z. Liu, C. Qiu, Negative refraction imaging of acoustic waves by a two-dimensional three-component phononic crystal, Physical Review B 73 (2006) 054302.
L. Fok, M. Ambati, X. Zhang, Acoustic metamaterials, MRS Bulletin 33 (2008) 931-934.
S. Zhang, L. Yin, N. Fang, Focusing ultrasound with an acoustic metamaterial network., Physical Review Letter 102 (2009) 194301.
M. Ambati, N. Fang, C. Sun, X. Zhang, Surface resonant states and superlensing in acoustic metamaterials, Physical Review B 75 (2007) 195447.
C. Goffaux, J. Sanchez-Dehesa, Two-dimensional phononic crystals studied using a variational method: Application to lattices of locally resonant materials, Physical Review B 67 (2003) 144301.
H. H. Huang, C. T. Sun, Wave attenuation mechanism in an acoustic metamaterial with negative effective mass density, New Journal of Physics 11 (2009) 013003.
H. H. Huang, C. T. Sun, G. L. Huang, On the negative effective mass density in acoustic metamaterials, International Journal of Engineering Science 47 (2009) 610-617.
R. Sainidou, N. Stefanou, I. E. Psarobas, A. Modinos, A layer-multiple-scattering method for phononic crystals and heterostructures of such, Computer Physics Communications 166 (2005) 197-240.
Y. Xiao, J. Wen, X. Wen, Flexural wave band gaps in locally resonant thin plates with periodically attached spring-mass resonators, Journal of Physics D: Applied Physics 45 (2012) 195401.
Y. Xiao, J. Wen, X. Wen, Longitudinal wave band gaps in metamaterial-based elastic rods containing multi-degree-of-freedom resonators, New Journal of Physics 14 (2012) 033042.
C. F. Beards, Engineering Vibration Analysis with Application to Vontrol Systems, Edward Arnold, London, 1995.
L. E. Kinsler, A. R. Frey, A. B. Coppens, J. V. Sanders, Fundamentals of Acoustics, 4th ed., John Wiley & Sons, New York, 2000.
D. Zwillinger, Standard Mathematical Tables and Formulae, 31st ed., CRC Press, New York, 2003.