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Research Papers

Vibration Characteristics of Metamaterial Beams With Periodic Local Resonances

[+] Author and Article Information
M. Nouh

Mechanical Engineering Department,
University of Maryland,
College Park, MD 20742

O. Aldraihem

Mechanical Engineering Department,
King Saud University,
Riyadh 11421, Saudi Arabia
King Abdulaziz City of Science and Technology,
P.O. Box 6086,
Riyadh 11442, Saudi Arabia

A. Baz

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

1Corresponding author.

Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received December 18, 2013; final manuscript received June 30, 2014; published online October 6, 2014. Assoc. Editor: Michael Leamy.

J. Vib. Acoust 136(6), 061012 (Oct 06, 2014) (12 pages) Paper No: VIB-13-1435; doi: 10.1115/1.4028453 History: Received December 18, 2013; Revised June 30, 2014

Vibration characteristics of metamaterial beams manufactured of assemblies of periodic cells with built-in local resonances are presented. Each cell consists of a base structure provided with cavities filled by a viscoelastic membrane that supports a small mass to form a source of local resonance. This class of metamaterial structures exhibits unique band gap behavior extending to very low-frequency ranges. A finite element model (FEM) is developed to predict the modal, frequency response, and band gap characteristics of different configurations of the metamaterial beams. The model is exercised to demonstrate the band gap and mechanical filtering capabilities of this class of metamaterial beams. The predictions of the FEM are validated experimentally when the beams are subjected to excitations ranging between 10 and 5000 Hz. It is observed that there is excellent agreement between the theoretical predictions and the experimental results for plain beams, beams with cavities, and beams with cavities provided with local resonant sources. The obtained results emphasize the potential of the metamaterial beams for providing significant vibration attenuation and exhibiting band gaps extending to low frequencies. Such characteristics indicate that metamaterial beams are more effective in attenuating and filtering low-frequency structural vibrations than plain periodic beams of similar size and weight.

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Figures

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Fig. 1

Configurations of idealized metamaterial structure (a) and beam with periodic local resonances (b)

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Fig. 2

(a) Finite element mesh of the metamaterial beam and (b) a schematic diagram of the single element

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Fig. 3

Periodic cells of the metamaterial beam

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Fig. 4

Schematic drawings of the different configurations of beams used in the experiments

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Fig. 5

Experimental prototype of metamaterial beam with periodic local resonances

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Fig. 6

Experimental setup of metamaterial beam with periodic local resonances under base excitation from a mechanical shaker

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Fig. 7

Experimentally measured storage modulus and loss factor of the VEM used in the metamaterial beam

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Fig. 8

Frequency response of the beam's tip deflection as a ratio of the base excitation over a 5 kHz range for (a) beam 2, (b) beam 3, (c) beam 4, and (d) beam 5 in comparison with beam 1

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Fig. 9

Frequency response of the beam's tip deflection as a ratio of the base excitation over a 500 Hz range for (a) beam 2, (b) beam 3, (c) beam 4, and (d) beam 5 in comparison with beam 1 (shaded areas show the large attenuation of the 4th bending mode in beams 4 and 5 compared to beams 2 and 3).

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Fig. 10

Magnitude of vibration attenuation in dB of metamaterial beams 2, 3, 4, and 5 compared to the vibration of plain beam 1

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Fig. 11

Laser vibrometer measurement of the vibration of a metamaterial beam with periodic local resonances under base excitation

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Fig. 12

Mode shapes for the first four natural frequencies of vibrations of beams 1, 2, 3, 4, and 5 (amplitudes given in m/s)

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Fig. 13

Comparison between the experimental and theoretical predictions of the mode shapes of beam 1 (amplitudes given in m/s)

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Fig. 14

Comparison between the experimental and theoretical predictions of the mode shapes of beam 4 (amplitudes given in m/s)

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Fig. 15

Real and imaginary parts (α and β) of the wave propagation constant reflecting the stop and pass bands for beam 4 in comparison to the experimental results

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Fig. 16

Real and imaginary parts (α and β) of the wave propagation constant reflecting the stop and pass bands for beam 5 in comparison to the experimental results

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