0
Research Papers

Active Acoustic Metamaterial With Simultaneously Programmable Density and Bulk Modulus

[+] Author and Article Information
W. Akl

Design and Production Engineering Department,
Ain Shams University,
Cairo, 11517, Egypt

A. Baz

Mechanical Engineering Department,
University of Maryland,
College Park, MD 20742
e-mail: baz@umd.edu

1Corresponding author.

Contributed by the Noise Control and Acoustics Division of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received August 25, 2011; final manuscript received October 4, 2012; published online March 28, 2013. Assoc. Editor: Lonny Thompson.

J. Vib. Acoust 135(3), 031001 (Mar 28, 2013) (17 pages) Paper No: VIB-11-1186; doi: 10.1115/1.4023141 History: Received August 25, 2011; Revised October 04, 2012

Acoustic metamaterials are those structurally engineered materials that are composed of periodic cells designed in such a fashion to yield specific material properties (density and bulk modulus) that would affect the wave propagation pattern within in a specific way. All the currently exerted efforts are focused on studying passive metamaterials with fixed material properties. In this paper, the emphasis is placed on the development of a new class of composite one-dimensional active acoustic metamaterials (CAAMM) with effective densities and bulk moduli that are programmed to vary according to any prescribed patterns along its volume. A cylindrical water-filled cylinder coupled to two piezoelectric elements form a composite cell to act as a base unit for a periodic metamaterial structure. Two different configurations are considered. In the first configuration, a piezoelectric panel is flash-mounted to the face of the cylinder, while the other is side-mounted to the cylinder wall, introducing a variable stiffness along the wave propagation path. In the second configuration, the face-mounted piezoelectric panel remains unchanged, while the side-mounted panel is replaced with an active Helmholtz resonator with piezoelectric base panel. A detailed theoretical lumped-parameter model for the two configurations is present, from which the stiffness of both active elements is controlled via charge feedback control to yield arbitrary homogenized effective bulk modulus and density over a very wide frequency range. Numerical examples are presented to demonstrate the performance characteristics of the proposed. The CAAMM presents a viable approach to the development of effective domains with a controllable wave propagation pattern to suit many applications.

Copyright © 2013 by ASME
Your Session has timed out. Please sign back in to continue.

References

Lapine, M., 2007, “The Age of Metamaterials,” Metamaterials, 1, p. 1. [CrossRef]
Shamonina, E., and Solymar, L., 2007, “Metamaterials: How the Subject Started,” Metamaterials, 1(1), pp. 12–18. [CrossRef]
Gil, M., Bonache, J., and Martín, F., 2008, “Metamaterial Filters: A Review,” Metamaterials, 2(4), pp. 186–197. [CrossRef]
Engheta, N., and Ziolkowski, R. W., 2006, Metamaterials: Physics and Engineering Explorations, Wiley-IEEE, New York.
Pendry, J. B., 2000, “Negative Refraction Makes a Perfect Lens,” Phys. Rev. Lett., 85(18), pp. 3966–3969. [CrossRef] [PubMed]
Pendry, J., Schurig, D., and Smith, D., 2006, “Controlling Electromagnetic Fields,” Science, 312(5781), pp. 1780–1782. [CrossRef] [PubMed]
Cummer, S. A., Popa, B. I., Schurig, D., Smith, D. R., and Pendry, J., 2006, “Full-Wave Simulations of Electromagnetic Cloaking Structures,” Phys. Rev. E, 74(3), p. 036621. [CrossRef]
Wu, Q., Zhang, K., Meng, F., and Li, L. W., 2009, “Material Parameters Characterization for Arbitrary N-Sided Regular Polygonal Invisible Cloak,” J. Phys. D: Appl. Phys., 42, p. 035408. [CrossRef]
Guenneau, S., Movchan, A., Pétursson, G., and Ramakrishna, S. A., 2007, “Acoustic Metamaterials for Sound Focusing and Confinement,” New J. Phys., 9, p. 399. [CrossRef]
Cervera, F., Sanchis, L., Sánchez-Perez, J., Martinez-Sala, R., Rubio, C., Meseguer, F., López, C., Caballero, D., and Sánchez-Dehesa, J., 2002, “Refractive Acoustic Devices for Airborne Sound,” Phys. Rev. Lett., 88, p. 023902. [CrossRef] [PubMed]
Climente, A., Torrent, D., and Sanchez-Dehesa, J., 2010, “Sound Focusing by Gradient Index Sonic Lenses,” Appl. Phys. Lett., 97, p. 104103. [CrossRef]
Sánchez-Dehesa, J., Garcia-Chocano, V., Torrent, D., Cervera, F., Cabrera, S., and Simon, S., 2011, “Noise Control by Sonic Crystal Barriers Made of Recycled Materials,” J. Acoust. Soc. Am., 129(3), pp. 1173–1183. [CrossRef] [PubMed]
Theodore, P., Nicholas, M., Orris, G., Cai, L., Torrent, D., and Sánchez-Dehesa, J., 2010, “Sonic Gradient Index Lens for Aqueous Applications,” Appl. Phys. Lett., 97, p. 113503. [CrossRef]
Torrent, D., and Sánchez-Dehesa, J., 2007, “Acoustic Metamaterials for New Two-Dimensional Sonic Devices,” New J. Phys., 9, p. 323. [CrossRef]
Sánchez-Pérez, J., Caballero, D., Mártinez-Sala, R., Rubio, C., Sánchez-Dehesa, J., Meseguer, F., Llinares, J., and Gálvez, F., 1998, “Sound Attenuation by a Two-Dimensional Array of Rigid Cylinders,” Phys. Rev. Lett., 80(24), pp. 5325–5328. [CrossRef]
Sanchis, L., Cervera, F., Sanchez-Dehesa, J., Sanchez-Perez, J., Rubio, C., and Martinez-Sala, R., 2001, “Reflectance Properties of Two Dimensional Sonic Band Gap Crystals,” J. Acoust. Soc. Am., 109, pp. 2598–2605. [CrossRef] [PubMed]
Sanchis, L., Hakansson, A., Cervera, F., and Sanchez-Dehesa, J., 2003, “Acoustic Interferometers Based on Two-Dimensional Arrays of Rigid Cylinders in Air,” Phys. Rev. B, 67, p. 035422. [CrossRef]
Lee, S. H., Park, C. M., Seo, Y. M., Wang, Z. G., and Kim, C. K., 2009, “Acoustic Metamaterial With Negative Density,” Phys. Lett. A, 373(48), pp. 4464–4469. [CrossRef]
Huang, H., Sun, C., and Huang, G., 2009, “On the Negative Effective Mass Density in Acoustic Metamaterials,” Int. J. Eng. Sci., 47(4), pp. 610–617. [CrossRef]
Yao, S., Zhou, X., and Hu, G., 2008, “Experimental Study on Negative Effective Mass in a 1D Mass–Spring System,” New J. Phys., 10, p. 043020. [CrossRef]
Cheng, Y., Xu, J., and Liu, X., 2008, “One-Dimensional Structured Ultrasonic Metamaterials With Simultaneously Negative Dynamic Density and Modulus,” Phys. Rev. B, 77(4), p. 045134. [CrossRef]
Milton, G. W., and Willis, J. R., 2007, “On Modifications of Newton's Second Law and Linear Continuum Elastodynamics,” Proc. R. Soc. London, 463(2079), p. 855. [CrossRef]
Chan, C., Li, J., and Fung, K., 2006, “On Extending the Concept of Double Negativity to Acoustic Waves,” J. Zhejiang Univ., Sci., 7(1), pp. 24–28. [CrossRef]
Li, J., and Chan, C., 2004, “Double-Negative Acoustic Metamaterial,” Phys. Rev. E, 70(5), p. 055602. [CrossRef]
Ding, Y., Liu, Z., Qiu, C., and Shi, J., 2007, “Metamaterial With Simultaneously Negative Bulk Modulus and Mass Density,” Phys. Rev. Lett., 99(9), p. 93904. [CrossRef]
Lee, S. H., Park, C. M., Seo, Y. M., Wang, Z. G., and Kim, C. K., 2009, “Acoustic Metamaterial With Negative Modulus,” J. Phys.: Condens. Matter, 21, p. 175704. [CrossRef] [PubMed]
Choi, S., and Kim, Y. H., 2002, “Sound-Wave Propagation in a Membrane–Duct (L),” J. Acoust. Soc. Am., 112, p. 1749. [CrossRef] [PubMed]
Chiu, Y., Cheng, L., and Huang, L., 2006, “Drum-Like Silencers Using Magnetic Forces in a Pressurized Cavity,” J. Sound Vib., 297(3–5), pp. 895–915. [CrossRef]
Esteve, S. J., and Johnson, M. E., 2005, “Adaptive Helmholtz Resonators and Passive Vibration Absorbers for Cylinder Interior Noise Control,” J. Sound Vib., 288(4–5), pp. 1105–1130. [CrossRef]
Nagaya, K., Hano, Y., and Suda, A., 2001, “Silencer Consisting of Two-Stage Helmholtz Resonator With Auto-Tuning Control,” J. Acoust. Soc. Am., 110, p. 289. [CrossRef]
Kostek, T. M., and Franchek, M. A., 2000, “Hybrid Noise Control in Ducts,” J. Sound Vib., 237(1), pp. 81–100. [CrossRef]
Akl, W., and Baz, A., 2010, “Multi-Cell Active Acoustic Metamaterial With Programmable Bulk Modulus,” J. Intell. Mater. Syst. Struct., 21, pp. 541–556. [CrossRef]
Akl, W., Smoker, J., and Baz, A., 2011, “Acoustic Metamaterial With Controllable Directivity and Dispersion Characteristics,” Proc. SPIE 7977, Active and Passive Smart Structures and Integrated Systems 2011, San Diego, CA, March 7–10, Paper No. 79771D. [CrossRef]
Baz, A., 2009, “The Structure of an Active Acoustic Metamaterial With Tunable Effective Density,” New J. Phys., 11, p. 123010. [CrossRef]
Baz, A., 2010, “An Active Acoustic Metamaterial With Tunable Effective Density,” ASME J. Vibr. Acoust., 132(4), pp. 1–9. [CrossRef]
Lighthill, J., 2001, Waves in Fluids, Cambridge University, Cambridge, UK.
Rossing, T. D., 2007, Springer Handbook of Acoustics, Springer-Verlag, Berlin.

Figures

Grahic Jump Location
Fig. 5

Uncontrolled homogenized bulk modulus and density for a cavity with face- and side-mounted flexible panels

Grahic Jump Location
Fig. 6

Electrical circuit analogous to the cavity with active panels

Grahic Jump Location
Fig. 7

Reduced electrical circuit analogous to the cavity with active panels

Grahic Jump Location
Fig. 8

(a),(c)–(b),(d) Stiffness and control voltage of side- and face-mounted panels. (e),(f) Resultant homogenized bulk modulus and density (20 times those of water).

Grahic Jump Location
Fig. 9

(a),(c)–(b),(d) Stiffness and control voltage of side- and face-mounted panels. (e),(f) Resultant homogenized bulk modulus and density (0.05 times those of water).

Grahic Jump Location
Fig. 10

Helmholtz resonator coupled to an acoustic cavity and a face-mounted panel. (a) Single main acoustic cavity. (b) Cavity divided in two equal sections.

Grahic Jump Location
Fig. 11

Electrical circuit analogous to the cavity with Helmholtz resonator and a face-mounted panel

Grahic Jump Location
Fig. 4

Electrical circuit analogous to the cavity with side- and face-mounted panel

Grahic Jump Location
Fig. 3

Acoustic cavity coupled to two flexible panels. (a) Single main acoustic cavity. (b) Cavity divided in two equal sections. (c) Flexible panel equivalent spring-mass system.

Grahic Jump Location
Fig. 2

Electric circuit analogy of an acoustic cavity coupled to a flexible panel

Grahic Jump Location
Fig. 1

Acoustic cavity coupled with a flexible panel

Grahic Jump Location
Fig. 12

Uncontrolled homogenized bulk modulus and density for a cavity with Helmholtz resonator and a face-mounted panel

Grahic Jump Location
Fig. 13

Electrical circuit analogous to the cavity with active Helmholtz resonator and face-mounted panel

Grahic Jump Location
Fig. 14

(a),(c)–(b),(d) Stiffness and control voltage of Helmholtz and face-mounted panels. (e),(f) Resultant homogenized bulk modulus and density (20 times those of water).

Grahic Jump Location
Fig. 15

(a),(c)–(b),(d) Stiffness and control voltage of Helmholtz and face-mounted panels. (e),(f) Resultant homogenized bulk modulus and density (0.05 times those of water).

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In