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Journal of Vibration and Acoustics | Volume 132 | Issue 3 | Research Paper
Research Papers

Band Gaps in a Multiresonator Acoustic Metamaterial

[+] Author and Article Information
G. L. Huang1

Department of Systems Engineering, University of Arkansas at Little Rock, Little Rock, AR 72204glhuang@ualr.edu

C. T. Sun

School of Aeronautics and Astronautics, Purdue University, W. Lafayette, IN 47907

1

Corresponding author.

J. Vib. Acoust 132(3), 031003 (Apr 14, 2010) (6 pages) doi:10.1115/1.4000784 History: Received March 11, 2009; Revised October 08, 2009; Published April 14, 2010; Online April 14, 2010
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In this study, we investigated dispersion curves and the band gap structure of a multiresonator mass-in-mass lattice system. The unit cell of the lattice system consists of three separate masses connected by linear springs. It was demonstrated that the band gaps can be shifted by varying the spring constant and the magnitude of the internal masses. By using the conventional monatomic (single mass) lattice model as an equivalent system, the effective mass was found to become negative for frequencies in the band gaps. An attempt was made to represent the two-resonator mass-in-mass lattice with a microstructure continuum model. It was found that the microstructure continuum model can capture the dispersive behavior and band gap structure of the original two-resonator mass-in-mass system.
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Grahic Jump Location
+Dispersion curves obtained from the microstructure continuum model compared with that from the two-resonator mass-in-mass lattice model: (a) acoustic mode and optic mode, and (b) third mode
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Dispersion curves obtained from the microstructure continuum model compared with that from the two-resonator mass-in-mass lattice model: (a) acoustic mode and optic mode, and (b) third mode
Figure 5

Dispersion curves obtained from the microstructure continuum model compared with that from the two-resonator mass-in-mass lattice model: (a) acoustic mode and optic mode, and (b) third mode

Grahic Jump Location
+Dimensionless effective mass meff/mst as a function of ω/ω0 (one-resonator: dotted line; two-resonator: solid line): (a) k3/k2=0.1 and (b) k3/k2=2.0
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Dimensionless effective mass meff/mst as a function of ω/ω0 (one-resonator: dotted line; two-resonator: solid line): (a) k3/k2=0.1 and (b) k3/k2=2.0
Figure 4

Dimensionless effective mass meff/mst as a function of ω/ω0 (one-resonator: dotted line; two-resonator: solid line): (a) k3/k2=0.1 and (b) k3/k2=2.0

Grahic Jump Location
+Nondimensionalized dispersion curves for mass-in-mass systems (a) m3/m2=1.0 and (b) m3/m2=5.0
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Nondimensionalized dispersion curves for mass-in-mass systems (a) m3/m2=1.0 and (b) m3/m2=5.0
Figure 3

Nondimensionalized dispersion curves for mass-in-mass systems (a) m3/m2=1.0 and (b) m3/m2=5.0

Grahic Jump Location
+Nondimensionalized dispersion curves for the one (solid line) and two-resonator (dash line) mass-in-mass systems with (a) k3/k2=0.01, (b) k3/k2=0.1, (c) k3/k2=2.0, and (d) k3/k2=5.0
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Nondimensionalized dispersion curves for the one (solid line) and two-resonator (dash line) mass-in-mass systems with (a) k3/k2=0.01, (b) k3/k2=0.1, (c) k3/k2=2.0, and (d) k3/k2=5.0
Figure 2

Nondimensionalized dispersion curves for the one (solid line) and two-resonator (dash line) mass-in-mass systems with (a) k3/k2=0.01, (b) k3/k2=0.1, (c) k3/k2=2.0, and (d) k3/k2=5.0

Grahic Jump Location
+The two-resonator mass-in-mass lattice structure
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The two-resonator mass-in-mass lattice structure
Figure 1

The two-resonator mass-in-mass lattice structure

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