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Research Papers

Dynamic Behavior of a Metamaterial Beam With Embedded Membrane-Mass Structures

[+] Author and Article Information
Jung-San Chen

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

I-Ting Chien

Department of Engineering Science,
National Cheng Kung University,
No.1, University Road,
Tainan City 701, Taiwan
e-mail: N96044345@mail.ncku.edu.tw

1Corresponding author.

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received July 2, 2017; final manuscript received October 5, 2017; published online October 20, 2017. Assoc. Editor: Yihui Zhang.

J. Appl. Mech 84(12), 121007 (Oct 20, 2017) (7 pages) Paper No: JAM-17-1349; doi: 10.1115/1.4038146 History: Received July 02, 2017; Revised October 05, 2017

Flexural propagation behavior of a metamaterial beam with circular membrane-mass structures is presented. Each cell is comprised of a base structure containing circular cavities filled by an elastic membrane with a centrally loaded mass. Numerical results show that there exist two kinds of bandgaps in such a system. One is called Bragg bandgap caused by structural periodicity; the other is called locally resonant (LR) bandgap caused by the resonant behavior of substructures. By altering the properties of the membrane-mass structure, the location of the resonant-type bandgap can be easily tuned. An analytical model is proposed to predict the lowest bandgap location. A good agreement is seen between the theoretical results and finite element (FE) results. Frequencies with negative mass density lie in the resonant-type bandgap.

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Figures

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Fig. 1

Coordinate system of a membrane with a concentrated mass

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Fig. 2

(a) A metamaterial beam with circular membrane-mass structures and (b) a unit cell of the metamaterial beam

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Fig. 3

Dispersion relation of the beam (a) with membrane-mass resonators and (b) without membrane-mass resonators

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Fig. 4

Mode shape at the initial frequency of the (a) first bandgap and (b) second bandgap

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Fig. 5

Dispersion relation of the metamaterial beam with varying (a) mass magnitude and (b) membrane tension

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Fig. 6

(a) Edge frequencies of the first bandgap with varying mass magnitude and (b) edge frequencies of the second bandgap with varying mass magnitude

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Fig. 7

(a) Edge frequencies of the first bandgap with varying membrane tension and (b) edge frequencies of the second bandgap with varying membrane tension

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Fig. 8

The dependence of resonant-type bandgaps on (a) membrane thickness and (b) membrane radius

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Fig. 9

Dispersion relation of the metamaterial beam with (a) two adjacent cells of different masses and (b) double-layer resonator (m = 0.126 g, 0.251 g)

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Fig. 10

Comparison of the metamaterial beam with single-layer resonators and with double-layer resonators: (a) first bandgap and (b) second bandgap (m = 0.251 g)

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Fig. 11

The initial frequency of the first bandgap with different (a) mass magnitudes and (b) membrane tensions

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Fig. 12

The initial frequency of the first bandgap with different (a) membrane thicknesses and (b) membrane radii

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Fig. 13

Dynamic effective mass density of the metamaterial beam with single-layer resonators (ρ¯ho=ρho⋅Tho)

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Fig. 14

Dynamic effective mass density of the metamaterial beam with double-layer resonators (ρ¯ho=ρho⋅Tho)

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Fig. 15

The FRF of the host beam and metamaterial beam

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Fig. 16

Frequency response of the metamaterial beam with three kinds of masses

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Fig. 17

Comparison between the beam with single-layer resonators and the one with double-layer resonators (m = 0.251 g)

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Fig. 18

The FRF of the metamaterial beam with double-layer resonators of identical masses or different masses

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