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Research Papers

Negative Effective Mass Density of One-Dimensional Hierarchical Metacomposite

[+] Author and Article Information
Xiyue An

Laboratory of Structural Analysis
for Defense Engineering and Equipment,
College of Mechanics and Materials,
Hohai University,
Nanjing 210098, China
State Key Laboratory of Mechanics
and Control of Mechanical Structures,
Nanjing University of Aeronautics and Astronautics,
Nanjing 210016, China

Fangfang Sun, Peishi Yu

Laboratory of Structural Analysis
for Defense Engineering and Equipment,
College of Mechanics and Materials,
Hohai University,
Nanjing 210098, China

Hualin Fan

Laboratory of Structural Analysis
for Defense Engineering and Equipment,
College of Mechanics and Materials,
Hohai University,
Nanjing 210098, China
SINOPEC Key Laboratory of Geophysics,
SINOPEC Geophysical Research Institute,
Nanjing 211103, China
e-mail: fhl02@mails.tsinghua.edu.cn

Shiping He

College of Power,
Naval University of Engineering,
Wuhan 430033, China
e-mail: 38019522@qq.com

Daining Fang

College of Engineering,
Peking University,
Beijing 100871, China
e-mail: fangdn@pku.edu.cn

1Corresponding authors.

Manuscript received October 22, 2014; final manuscript received December 26, 2014; published online January 23, 2015. Editor: Yonggang Huang.

J. Appl. Mech 82(3), 031002 (Mar 01, 2015) (8 pages) Paper No: JAM-14-1491; doi: 10.1115/1.4029488 History: Received October 22, 2014; Revised December 26, 2014; Online January 23, 2015

A theoretical model of one-dimensional (1D) hierarchical metacomposite with internal resonators was proposed to generate negative effective mass over specific frequency ranges. Different from the single-resonator microstructure, the current hierarchical metamaterial with multilevel resonators was constructed by a series of springs and rigid bodies. The general formula of the current hierarchical metamaterial model was induced to reveal the relationship between the effective mass and the forcing frequency. It is found that the hierarchical metamaterial with multilevel resonators generates multifrequency band gaps with negative effective masses. The number of the band gaps equals to the order of the hierarchy. The total bandwidth for the negative effective mass increases with the hierarchy, meanwhile increasing the mass ratio can also obviously increase the bandwidth generating negative effective mass.

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Figures

Grahic Jump Location
Fig. 1

(a) 1D hierarchical metacomposite and (b) representation by an equivalent mass

Grahic Jump Location
Fig. 2

Effective mass of (a) single-resonator model, (b) dual-resonator model, (c) triresonator model, and (d) quad-resonator model at α=0.5 and β=0.5

Grahic Jump Location
Fig. 3

Triresonator model and the equivalent mass

Grahic Jump Location
Fig. 4

Effective mass of dual-resonator metacomposite when (a) increasing coefficient of stiffness ratio α; (b) increasing coefficient of mass ratio β; and (c) when M = 50 k1, α = 0.5 and β = 0.5

Grahic Jump Location
Fig. 5

Wave propagation model of the triresonator hierarchical metacomposite

Grahic Jump Location
Fig. 6

Dispersion curves of (a) single-resonator model, (b) dual-resonator model, (c) triresonator model, and (d) quad-resonator model

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