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Technical Brief

Wide Band-Gaps in Flexural Periodic Beams With Separated Force and Moment Resonators

[+] Author and Article Information
Michael Yu Wang

Department of Mechanical Engineering,
National University of Singapore,
Singapore 117575, Singapore;
Faculty of Engineering,
The Chinese University of Hong Kong,
Shatin, NT, Hong Kong
e-mail: michael.wang@nus.edu.sg

Yan Ting Choy, Choi Wah Wan

Faculty of Engineering,
The Chinese University of Hong Kong,
Shatin, NT, Hong Kong

Allen Song Zhao

College of Engineering,
University of Michigan,
Ann Arbor, MI 48109

Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received December 4, 2014; final manuscript received August 26, 2015; published online October 8, 2015. Assoc. Editor: Mahmoud Hussein.

J. Vib. Acoust 137(6), 064504 (Oct 08, 2015) (6 pages) Paper No: VIB-14-1455; doi: 10.1115/1.4031519 History: Received December 04, 2014; Revised August 26, 2015

As a locally resonant (LR) elastic system, a uniform Euler–Bernoulli beam suspended with force and moment resonators has complicated band-gap mechanisms and richer dispersive characteristics. In this paper, we consider the use of the force and moment resonators in a noncollocated manner. On the LR beam, the force-type vibrators and the moment-type vibrators are alternatingly arranged, with a separation distance. We present an analytical study of the dispersion characteristics of the LR system, especially the effects of the separation distance on further widening the frequency stop bands. In addition, the complex dispersion properties on the frequency axis are described using a formulation different from the common approach.

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Figures

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Fig. 1

The separated force and moment resonators periodically attached on an Euler–Bernoulli beam

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Fig. 6

Dispersion curves in the α–β plane, with changing Ω starting at point A, Ω = 0 : (a) Ω01 = Ω02 = 0.5 and (b) Ω01 = Ω02 = 1.0

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Fig. 5

In the α–β plane, the four types of frequency dispersion regions and their associated transition types are as defined by the curves p, r, and s. At point A, Ω = 0.

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Fig. 2

The frequency band-gaps of the example with Ω01=Ω02=Ω0, γ1=γ2=0.5, and δ=0.25, for b1=0, 1/6, 1/3,  and 1/2 , respectively. BS band-gaps are in light shade (blue color) and LR band-gaps are in dark shade (red color).

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Fig. 3

The frequency band-gaps of the example with Ω01=Ω02=Ω0, γ1=γ2=2.0, and δ=0.40, for b1=0,  0.1,  0.25, and 0.5, respectively. BS band-gaps are in light shade (blue color) and LR band-gaps are in dark shade (red color).

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Fig. 4

Wide band-gaps of the example with Ω01 = Ω02 = Ω0, γ1 = γ2 = 2.0,δ = 0.40, and b1 = 0.235: (a) BS band-gaps are in light shade (blue color) and LR band-gaps are in dark shade (red color) and (b) the frequency edges of the band-gaps as defined by the curves p, r, and s, respectively

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