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Research Papers

Nonlocal Homogenization Model for Wave Dispersion and Attenuation in Elastic and Viscoelastic Periodic Layered Media

[+] Author and Article Information
Ruize Hu

Department of Civil and
Environmental Engineering,
Vanderbilt University,
Nashville, TN 37235
e-mail: ruize.hu@vanderbilt.edu

Caglar Oskay

Department of Civil and
Environmental Engineering,
Vanderbilt University,
Nashville, TN 37235
e-mail: caglar.oskay@vanderbilt.edu

1Corresponding author.

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received October 17, 2016; final manuscript received November 29, 2016; published online January 12, 2017. Assoc. Editor: Shaoxing Qu.

J. Appl. Mech 84(3), 031003 (Jan 12, 2017) (12 pages) Paper No: JAM-16-1503; doi: 10.1115/1.4035364 History: Received October 17, 2016; Revised November 29, 2016

This manuscript presents a new nonlocal homogenization model (NHM) for wave dispersion and attenuation in elastic and viscoelastic periodic layered media. Homogenization with multiple spatial scales based on asymptotic expansions of up to eighth order is employed to formulate the proposed nonlocal homogenization model. A momentum balance equation, nonlocal in both space and time, is formulated consistent with the gradient elasticity theory. A key contribution in this regard is that all model coefficients including high-order length-scale parameters are derived directly from microstructural material properties and geometry. The capability of the proposed model in capturing the characteristics of wave propagation in heterogeneous media is demonstrated in multiphase elastic and viscoelastic materials. The nonlocal homogenization model is shown to accurately predict wave dispersion and attenuation within the acoustic regime for both elastic and viscoelastic layered composites.

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Figures

Grahic Jump Location
Fig. 2

Unit cell of the microstructure: (a) elastic bilayer and (b) viscoelastic four-layered

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Fig. 1

Recursive influence function generation procedure

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Fig. 7

Responses at two time instances under step loading: (a) t = 0.1 ms and (b) t = 0.15 ms

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Fig. 3

Dispersion relation of NHM6 and the reference solution for bilayer microstructure

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Fig. 4

Error in the prediction of the stop band: (a) Al-metal stop band initiation, (b) Al-metal stop band end, (c) Al-polymer stop band initiation, and (d) Al-polymer stop band end

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Fig. 5

Dispersion curves of NHM2, NHM4, and NHM6 compared to the reference model

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Fig. 12

Transmitted wave amplitude of elastic and viscoelastic composite computed by NHM6

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Fig. 6

Dispersion curve of NHM6 compared to the gradient elasticity model

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Fig. 8

Displacement histories at x = 0.9L under sinusoidal loading at frequencies: (a) 132.71 kHz and (b) 221.18 kHz

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Fig. 9

Transmitted wave amplitude at x = 0.9L at frequency between 10 kHz and 442.4 kHz

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Fig. 10

Transmitted wave amplitude at x=0.9L for the four-layered viscoelastic composite at frequency between 1 kHz and 50 kHz

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Fig. 11

Displacement histories of viscoelastic composite at x = 0.9L under sinusoidal loading at frequencies: (a) 15 kHz and (b) 25 kHz

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