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TECHNICAL BRIEFS

Quasi-One-Dimensional Periodic Structure with Locally Resonant Band Gap

[+] Author and Article Information
Gang Wang1

Institute of Mechatronical Engineering,  National University of Defense Technology, Changsha 410073, China and PBG Research Center,  National University of Defense Technology, Changsha 410073, Chinawang–g@vip.sina.com

Xisen Wen, Jihong Wen, Yaozong Liu

Institute of Mechatronical Engineering,  National University of Defense Technology, Changsha 410073, China and PBG Research Center,  National University of Defense Technology, Changsha 410073, China

1

Corresponding author.

J. Appl. Mech 73(1), 167-170 (May 12, 2005) (4 pages) doi:10.1115/1.2061947 History: Received July 14, 2004; Revised May 12, 2005

The propagation of longitudinal elastic waves in quasi one-dimensional structure consisting of harmonic oscillators periodically jointed on a slender beam is studied. Sub-frequency locally resonant band gap with highly asymmetric attenuation is observed in both theoretical and experimental results, and both results match well. The stiffness and mass ratios are found analytically as two factors that influence the actual attenuation in the band gap of the locally resonant phononic crystals. The study on the weights of the two factors shows that the stiffness ratio is the key one. Thus, the reason for the mismatch between the regions of the sharp attenuation and the theoretical band gap in the locally resonant phononic crystals is discovered.

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Copyright © 2006 by American Society of Mechanical Engineers
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Figures

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Figure 1

(a) Quasi-one-dimensional phononic crystal composed of infinitely extended continuous slender beam with periodically jointed harmonic oscillators. We consider the longitudinal waves propagating along x direction. (b) The actual sample of the quasi-one-dimensional phononic crystal with eight periods and the experimental instruments.

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Figure 2

(a) Calculated attenuation and phase constants μ,ε of the quasi-1D LR PCs illustrated in Fig. 1 for several frequencies that are given in the normalized units βLx∕2π and Hz on the upper and lower abscissas, respectively. (b) Measured (solid line for the sample with eight periods, and dots for that with six periods) and calculated (dashed line for the sample with eight periods) transmission frequency response function for this quasi-1D LR PC. The subfigure illustrates a zoom from 1500 to 1600 Hz in order to give a clear description the eight peaks corresponding to the natural frequencies.

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Figure 3

The partial derivative of cosh(μmid) on the stiffness ratio k:K (upper line) and the mass ratio m:M (lower line) for several (a) mass and (b) stiffness ratios

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