Abstract
In this study, a laboratory method to evaluate the effective dynamic properties for flexural vibrations of a meta-structure is presented. The flexural vibration of a beam with periodically spaced resonators was investigated using wave propagation analysis. After analyzing vibration interactions between the resonators and the homogeneous beam, the effective dynamic properties of the meta-structure were evaluated using the transfer function method. The comparison of the measured and predicted results allowed for an understanding of the proposed vibration control mechanism. The effective bending stiffness was not affected by the attached resonators. The effective mass exhibited significant frequency-dependent variation near the natural frequency of the resonators. The effective mass becomes complex when the stiffness of the resonators is viscoelastic. The reflected wave from the metamaterial was completely blocked when the real part of the effective mass became negative. The effective mass decreased as the loss factor of the attached resonators increased. The proposed evaluation method can be used to analyze the effects of resonators on structural vibrations.
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Liu Z, Zhang X, Mao Y, Zhu YY, Yang Z, Chan CT, Sheng P (2000) Locally resonant sonic materials. Science 289:1734–1736. doi:10.1126/science.289.5485.1734
Fang N, Xi D, Xu J, Ambati M, Srituravanich W, Sun C, Zhang X (2006) Ultrasonic metamaterials with negative modulus. Nat Mater 5:452–456. doi:10.1038/nmat1644
Liu A, Zhou X, Huang G, Hu G (2012) Super-resolution imaging by resonant tunneling in anisotropic. J Acoust Soc Am 132:2800–2806. doi:10.1121/1.4744932
Mei J, Ma G, Yang M, Wen W, Sheng P (2012) Dark acoustic metamaterials as super absorbers for low frequency sound. Nature Commun 3:756. doi:10.1038/ncomms1758
Seo Y, Park J, Lee S, Park C, Kim C, Lee S (2012) Acoustic metamaterial exhibiting four different sign combiations of density and modulus. J Appl Phys 111:023504. doi:10.1063/1.3676262
Hao L, Ding C, Zhao S (2012) Tunable acoustic metamaterial with negative modulus. J Appl Phys A 106:807–811. doi:10.1007/s00339-011-6682-8
Zhang H, Wen J, Xiao Y, Wang G, Wen X (2015) Sound transmission loss of metamaterial thin plates with periodic subwavelength arrays of shunted piezoelectric patches. J Sound Vib 343:104–120. doi:10.1016/j.jsv.2015.01.019
Pai PF, Peng H, Jiang S (2014) Acoustic metamaterial beams based on multi-frequency vibration absrobers. Int J Mech Sci 79:195–205. doi:10.1016/j.ijmecsci.2013.12.013
Cummer SA, Schurig D (2007) One path to acoustic cloaking. New J Phys 9:45. doi:10.1088/1367-2630/9/3/045
Zhang S, Xia C, Fang N (2011) Broadband acoustic cloak for ultrasound waves. Phys Rev Lett 106:024301. doi:10.1103/PhysRevLett.106.024301
Norris AN, Shuvalov AL (2011) Elastic cloaking theory. Wave Motion 49:525–538. doi:10.1016/j.wavemoti.2011.03.002
Torrent D, Sánchez-Dehesa J (2008) Acoustic cloaking in two dimensions: a feasible approach. New J Phys 10:063015. doi:10.1088/1367-2630/10/6/063015
Bigoni D, Guenneau S, Movchan A, Prun M (2013) Elastic metamaterials with inertial locally resonant structure: APPLICATION to lensing and localization. Phys Rev B 87:174303. doi:10.1103/PhysRevB.87.174.303
Li Y, Yu G, Liang B, Zou X, Li G, Cheng S, Cheng J (2014) Three-dimensional ultrathin planar lenses by acoustic metamaterials. Sci Rep 4:6830. doi:10.1038/srep06830
Layman CN, Martin TP, Moore KM, Calvo DC, Orris GJ (2011) Designing acoustic transformation devices using fluid homogenization of an elastic substructure. Appl Phys Lett 99:163503. doi:10.1063/1.3652914
Smith DR, Schultz S (2002) Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients. Phys Rev B 65:195104. doi:10.1103/PhysRevB.65.195104
Chen X, Grzegorczyk TM, Wu B-I, Pacheco J, Jr, Kong JA (2004) Robust method to retrieve the constitutive effective parameters of metamaterials. Phys Rev E 70:016608. doi:1103/PhysRevE.70.016608
Fokin V, Ambati M, Sun C, Zhang X (2007) Method for retrieving effective properties of locally resonant acoustic metamaterials. Phys Rev B 76:144302. doi:10.1103/PhysRevB.76.144302
Xiao Y, Weon J, Yu D, Wen X (2013) Flexural wave propagation in beams with periodically attached vibration absorbers: band-gap behavior and band formation mechanisms. J Sound Vib 332:867–893. doi:10.1016/j.jsv.2012.09.035
Bigoni D, Gei M, Movchan AB (2008) Dynamics of a prestressed stiff layer on an elastic half space: filtering and band gap characteristics of periodic structural models derived from long-wave asymptotics. J Mech Phys Solids 56:2494–2520. doi:10.1016/j.jmps.2008.02.007
Ferry JD (1980) Viscoelastic properties of polymers. Wiley, New York
Pritz T (1982) Transfer function method for investigating the complex modulus of acoustic materials: rod-like specimen. J Sound Vib 81:359–376. doi:10.1016/0022-460X(82)90245-0
ANSI (1998) ANSI S2.22-1998. Resonance method for measuring the dynamic mechanical properties of viscoelastic materials. American National Standards Institute, published through the Acoustical Society of America (New York)
Park J (2005) Transfer function methods to measure dynamic mechanical properties of complex structures. J Sound Vib 288:57–79. doi:10.1016/j.jsv.2004.12.019
Park J (2005) Measurements of the frame acoustic properties of porous and granular materials. J Acoust Soc Am 118:3483–3490. doi:10.1121/1.2130929
Park J, Park B, Kim D, Park J (2012) Determination of effective mass density and modulus for resonant metamaterials. J Acoust Soc Am 132:2793–2799. doi:10.1121/1.4744940
Misseroni D, Colquitt DJ, Movchan AB, Movchan NV, Jones IS (2016) Cymatics for the cloaking of flexural vibrations in a structured plate. Sci Rep 6:23929. doi:10.1038/srep23929
Wang YF, Wang YS, Laude V (2015) Wave propagation in two-dimensional viscoelastic metamaterials. Phys Rev B 92:104110. doi:10.1103/PhysRevB.92.104110
Wang T, Sheng MP, Qin QH (2015) Multi-flexural band gaps in an Euler-Bernoulli beam with lateral local resonators. Phys Lett A 380:525–529. doi:10.1016/j.physleta.2015.12.010
Blevins RD (1990) Flow-induced vibration. Krieger Publishing Company, Florida
Fahy FJ (1985) Sound and structural vibration. Academic, London
Song BH, Bolton JS (2000) A transfer-matrix approach for estimating the characteristic impedance and wave numbers of limp and rigid porous materials. J Acoust Soc Am 107:1131–1152. doi:10.1121/1.428404
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This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (2016R1A2B4013054).
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Yang, W., Kim, B., Cho, S. et al. Experimental Method to Evaluate Effective Dynamic Properties of a Meta-Structure for Flexural Vibrations. Exp Mech 57, 417–425 (2017). https://doi.org/10.1007/s11340-016-0242-2
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DOI: https://doi.org/10.1007/s11340-016-0242-2