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Research Papers

Wave Propagation in Sandwich Structures With Multiresonators

[+] Author and Article Information
J. S. Chen

Department of Engineering Science,
National Cheng Kung University,
No. 1, University Road,
Tainan City 701, Taiwan
e-mail: jschen273@mail.ncku.edu.tw

Y. J. Huang

Department of Engineering Science,
National Cheng Kung University,
No. 1, University Road,
Tainan City 701, Taiwan
e-mail: n96034285@mail.ncku.edu.tw

1Corresponding author.

Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received September 14, 2015; final manuscript received March 2, 2016; published online May 23, 2016. Assoc. Editor: Mahmoud Hussein.

J. Vib. Acoust 138(4), 041009 (May 23, 2016) (10 pages) Paper No: VIB-15-1385; doi: 10.1115/1.4033197 History: Received September 14, 2015; Revised March 02, 2016

A new sandwich beam with embedded multiresonators is presented. Two continuum Timoshenko beam models are adopted for modeling sandwich beams. Numerical results show that multiple resonators can lead to multiple resonant-type bandgaps with remarkable wave attenuation. The effective mass is found to become negative for frequencies in the bandgaps where the wave is greatly attenuated. With two identical resonators connected in parallel, only one single bandgap can be found. If two resonators with equal masses and springs are connected in series, the central frequency of the second bandgap is approximated twice of the central frequency of the first gap. For the beam with series-connected resonators, a simple two degrees-of-freedom system is proposed and used for predicting the initial frequencies of the bandgaps while for the beam with resonators in parallel, two separate single degree-of-freedom systems are introduced.

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References

Figures

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Fig. 1

(a) Model I: a sandwich beam with resonators in series and (b) model II: a sandwich beam with resonators in parallel

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Fig. 2

Sketch of a unit cell (left) and its equivalent model (right) for (a) model I and (b) model II

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Fig. 3

A two degrees-of-freedom system

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Fig. 6

Attenuation factor β for the sandwich beam with resonators in series (model I) (a) k2/k1=0.5; (b) k2/k1=1.0; and (c) k2/k1=1.5 (a = 0.012 m, m2/m1=1.0)

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Fig. 5

Attenuation factor β for the sandwich beam with resonators in series (model I) (a) m2/m1=0.5; (b) m2/m1=1.0; and (c) m2/m1=1.5 (a = 0.012 m, k2/k1=1.0)

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Fig. 17

Effect of k2/k1 for model II on edge frequencies of (a) the first bandgap and (b) the second bandgap (a = 0.012 m, m2/m1=1.0)

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Fig. 18

Effect of a for model II on edge frequencies of (a) the first bandgap and (b) the second bandgap (m2/m1=0.5, k2/k1=1.0)

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Fig. 19

Dispersion curves for model II, obtained by the continuum model and FE model (a = 0.012 m, m2/m1=1.5, k2/k1=1.0)

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Fig. 7

Effect of m2/m1 for model I on edge frequencies of (a) the first bandgap and (b) the second bandgap (a = 0.012 m, k2/k1=1.0)

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Fig. 8

Effect of k2/k1 for model I on edge frequencies of (a) the first bandgap and (b) the second bandgap (a = 0.012 m, m2/m1=1.0)

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Fig. 9

Effect of a for model I on edge frequencies of (a) the first bandgap and (b) the second bandgap (m2/m1=0.5, k2/k1=1.0)

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Fig. 15

Comparison of attenuation factor β for the sandwich beam having a two-resonator system with m2/m1=1.0 and k2/k1=1.0 (model II) and for the beam with one spring–mass system (a = 0.012 m)

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Fig. 16

Effect of m2/m1 for model II on edge frequencies of (a) the first bandgap and (b) the second bandgap (a = 0.012 m, k2/k1=1.0)

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Fig. 20

Nondimensionalized wave number for model II as a function of dimensionless frequency ω¯, obtained by the continuum model with distributed masses and the one with effective mass (a = 0.012 m, m2/m1=1.5, k2/k1=1.0)

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Fig. 21

Dimensionless effective mass per unit length for model II with varying (a) m2/m1 and (b) k2/k1 (a = 0.012 m)

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Fig. 4

Two spring–mass systems

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Fig. 10

Dispersion curves for model I, obtained by the continuum model and finite element (FE) model (a = 0.012 m, m2/m1=1.5, k2/k1=1)

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Fig. 11

Nondimensionalized wave number for model I as a function of dimensionless frequency ω¯, obtained by the continuum model with distributed masses and the one with effective mass (a = 0.012 m, m2/m1=1.5, k2/k1=1)

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Fig. 12

Dimensionless effective mass per unit length for model I with varying (a) m2/m1 and (b) k2/k1 (a = 0.012 m)

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Fig. 13

Attenuation factor β for the sandwich beam with resonators in parallel (model II) (a) m2/m1=0.5 and (b) m2/m1=1.5 (a = 0.012 m, k2/k1=1.0)

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Fig. 14

Attenuation factor β for the sandwich beam with resonators in parallel (model II) (a) k2/k1=0.5 and (b) k2/k1=1.5 (a = 0.012 m, m2/m1=1.0)

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