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Research Papers

Band-Gap Properties of Elastic Metamaterials With Inerter-Based Dynamic Vibration Absorbers

[+] Author and Article Information
Xiang Fang, Kuo-Chih Chuang, Xiaoling Jin

Key Laboratory of Soft Machines and
Smart Devices of Zhejiang Province,
Department of Engineering Mechanics,
Zhejiang University,
Hangzhou 310027, China

Zhilong Huang

Key Laboratory of Soft Machines and
Smart Devices of Zhejiang Province,
Department of Engineering Mechanics,
Zhejiang University,
Hangzhou 310027, China
e-mail: zlhuang@zju.edu.cn

1Corresponding author.

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received January 30, 2018; final manuscript received April 5, 2018; published online May 10, 2018. Assoc. Editor: Pedro Reis.

J. Appl. Mech 85(7), 071010 (May 10, 2018) (9 pages) Paper No: JAM-18-1062; doi: 10.1115/1.4039898 History: Received January 30, 2018; Revised April 05, 2018

In this paper, inerter-based dynamic vibration absorbers (IDVAs) are applied in elastic metamaterials to broaden low-frequency band gaps. A discrete mass-spring lattice system and a distributed metamaterial beam carrying a periodic array of IDVAs are, respectively, considered. The IDVA consists of a spring and an inerter connected to a traditional mass-spring resonator. Compared to the traditional resonators, the special designed IDVAs generate two local-resonance (LR) band gaps for the discrete lattice system, a narrow low-frequency band gap and a wider high-frequency one. For the distributed IDVA-based metamaterial beam, in addition to the generated two separated LR band gaps, the Bragg band gap can also be significantly broadened and the three band gaps are very close to each other. Being able to amplify inertia, the IDVAs can be relatively light even operated for opening up low-frequency band gaps. When further introducing a dissipative damping mechanism into the IDVA-based metamaterials, the two close-split LR band gaps in the lattice system are merged into one wide band gap. As for the metamaterial beam with the dissipative IDVAs, an even wider band gap can be acquired due to the overlap of the adjacent LR and Bragg-scattering band gaps.

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Figures

Grahic Jump Location
Fig. 2

Three configurations of IDVAs: (a) IDVA1 (nondissipative), (b) IDVA2 (dissipative), and (c) IDVA3 (dissipative)

Grahic Jump Location
Fig. 1

A mass-spring lattice system carrying a periodic array of IDVAs

Grahic Jump Location
Fig. 4

Effects of inertance on the boundary of the band gaps of IDVA1

Grahic Jump Location
Fig. 3

Nondimensional dispersion curve of the lattice system carrying a periodic array of TLRs or IDVA1: (a) imaginary part of μ (band structure) and (b) real part of μ

Grahic Jump Location
Fig. 5

(a) Longitudinal wave attenuation constant for the lattice system carrying IDVA2 with different damping ratios. (b) Displacement transmissions of the 30-cell lattice system carrying IDVA2 with different damping ratios.

Grahic Jump Location
Fig. 6

(a) Longitudinal wave attenuation constant for the lattice system carrying IDVA3 with different damping ratios. (b) Displacement transmission of the 30-cell lattice system carrying IDVA3 with different damping ratios.

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Fig. 7

Metamaterial beam carrying a periodic array of IDVAs

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Fig. 8

Unit cell of metamaterial beam carrying different IDVAs: (a) IDVA1, (b), IDVA2, and (c) IDVA3

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Fig. 9

(a) Minimum real part of μ for the nondissipative infinite metamaterial beam attached with IDVA1. (b) Imaginary part of μ for the nondissipative infinite metamaterial beam attached with IDVA1.

Grahic Jump Location
Fig. 10

Minimum flexural wave attenuation constant for the infinite metamaterial beam carrying TLRs with different damping ratios

Grahic Jump Location
Fig. 11

(a) Minimum flexural wave attenuation constant for the infinite metamaterial beam carrying IDVA2 with different damping ratios. (b) Displacement transmissions of the ten-cell metamaterial beam carrying a periodic array of IDVA2 with different damping ratios.

Grahic Jump Location
Fig. 12

(a) Minimum flexural wave attenuation constant for the infinite metamaterial beam carrying IDVA3 with different damping ratios. (b) Displacement transmission of the ten-cell metamaterial beam carrying a periodic array of IDVA3 with different damping ratios.

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