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Research Papers

A Dispersive Nonlocal Model for In-Plane Wave Propagation in Laminated Composites With Periodic Structures

[+] Author and Article Information
H. Brito-Santana

Institute of Engineering Mechanics,
Beijing Jiaotong University,
Beijing 100044, China
e-mail: hbritosantana@gmail.com

Yue-Sheng Wang

Institute of Engineering Mechanics,
Beijing Jiaotong University,
Beijing 100044, China
e-mail: yswang@bjtu.edu.cn

R. Rodríguez-Ramos

Faculty of Mathematics and Computing Sciences,
University of Havana,
San Lázaro esq. L,
Vedado, Havana CP10400, Cuba
e-mail: reinaldo@matcom.uh.cu

J. Bravo-Castillero

Faculty of Mathematics and Computing Sciences,
University of Havana,
San Lázaro esq. L,
Vedado, Havana CP10400, Cuba
e-mail: jbravo@matcom.uh.cu

R. Guinovart-Díaz

Faculty of Mathematics and Computing Sciences,
University of Havana,
San Lázaro esq. L,
Vedado, Havana CP10400, Cuba
e-mail: guino@matcom.uh.c

Volnei Tita

Department of Aeronautical Engineering,
Engineering School of São Carlos,
University of São Paulo,
Av. João Dagnone,
São Carlos, Sao Paulo 1100, Brazil
e-mail: voltita@sc.usp.br

Manuscript received December 3, 2014; final manuscript received January 9, 2015; published online February 9, 2015. Editor: Yonggang Huang.

J. Appl. Mech 82(3), 031006 (Mar 01, 2015) (15 pages) Paper No: JAM-14-1562; doi: 10.1115/1.4029603 History: Received December 03, 2014; Revised January 09, 2015; Online February 09, 2015

In this paper, the problem of in-plane wave propagation with oblique incidence of the wave in an isotropic bilaminated composite under perfect contact between the layers and periodic distribution between them is studied. Based on an asymptotic dispersive method for the description of the dynamic processes, the dispersion equations were derived analytically from the average model. Numerical examples show that the dispersion curves obtained from the present model agree with the exact solutions for a range of wavelengths. Detailed numerical simulations are provided to illustrate graphically the phase and group velocities. Such illustrations allow the identification and comparison of the effects of the unit cell size, wave number and incident angle. It was observed that, as the incident angle increases, the dimensionless quasi-longitudinal phase velocity increases, and the dimensionless quasi-shear phase velocity decreases. In addition, the phase and group velocities decrease as the size of the unit cell increases. The frequency band structure, as a function of the wave-vector components is calculated.

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References

Figures

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Fig. 1

The layered composite and the unit cell. (a) Bilayered composite and (b) unit cell.

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Fig. 4

Slowness curves 1/VI for values of wave number κ = 2 and 6 m-1 with sizes of the unit cell, from the inside out: ε = 0 (solid black), 0.03 (dashed-dotted), 0.06 (dashed black), 0.08 (solid gray), and 0.1 (dashed gray)

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Fig. 5

Slowness curves 1/VII for values of wave number κ = 4 and 8 m-1 with sizes of the unit cell, from the inside out: ε = 0 (solid black), 0.03 (dashed-dotted), 0.06 (dashed black), 0.08 (solid gray), and 0.1 (dashed gray)

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Fig. 6

Angular dependence of the dimensionless phase velocities VI/V0I and VII/V0II for different sizes of the unit cell (ɛ = 0.03, 0.06, and 0.09) with the dimensionless wave number κl1 = 2

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Fig. 7

Dispersion relations VI/V0I and VII/V0II versus κl1 for different values of the incident angle (θ = 30 deg, 45 deg, and 60 deg) and different sizes of the unit cell (ɛ = 0.03, 0.06, and 0.09)

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Fig. 8

Group velocity VgI versus κl1 for different values of the incident angle (θ = 30 deg, 45 deg, and 60 deg) and different sizes of the unit cell (ɛ = 0.03, 0.06, and 0.09)

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Fig. 9

Group velocity VgII versus κl1 for different values of the incident angle (θ = 30 deg, 45 deg, and 60 deg) and different sizes of the unit cell (ɛ = 0.03, 0.06, and 0.09)

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Fig. 2

Comparison of the dispersion curves produced by the present model with the results from the micro-inertia model for μ1/μ2 = 10 and γ = 0.8: (a) longitudinal wave propagation normal to the direction of the layers and (b) transverse shear propagation normal to the direction of the layers

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Fig. 3

Comparison of the dispersion curves produced by the present model with the results from the micro-inertia model for μ1/μ2 = 100 and γ = 0.8: (a) longitudinal wave propagation normal to the direction of the layers and (b) transverse shear propagation normal to the direction of the layers

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Fig. 10

The difference Vg - V versus κl1 for different sizes of the unit cell (ɛ = 0.03, 0.06, and 0.09) with incident angle θ = 45 deg

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Fig. 11

Contours of constant frequency (in MHz) and group-velocity vectors for longitudinal wave propagation with different sizes of the unit cell (ɛ = 0, 0.03, 0.06, and 0.09)

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Fig. 12

Contours of constant frequency (in MHz) and group-velocity vectors for transverse shear propagation with different sizes of the unit cell (ɛ = 0, 0.03, 0.06, and 0.09)

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