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Research Papers

Wave Propagation Through a Micropolar Slab Sandwiched by Two Elastic Half-Spaces

[+] Author and Article Information
Peng Zhang, Yueqiu Li

Department of Applied Mechanics,
University of Sciences and Technology Beijing,
Beijing 100083, China

Peijun Wei

Department of Applied Mechanics,
University of Sciences and Technology Beijing,
Beijing 100083, China;
State Key Laboratory of Nonlinear
Mechanics (LNM),
Chinese Academy of Science,
Beijing 100080, China
e-mail: weipj@ustb.edu.cn

1Corresponding author.

Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received September 1, 2015; final manuscript received March 8, 2016; published online May 23, 2016. Assoc. Editor: Michael Leamy.

J. Vib. Acoust 138(4), 041008 (May 23, 2016) (17 pages) Paper No: VIB-15-1359; doi: 10.1115/1.4033198 History: Received September 01, 2015; Revised March 08, 2016

The problem of wave propagation through a micropolar elastic slab sandwiched by two classical elastic half-spaces is studied in this paper. Different from the classical elastic solids, the particle in micropolar solids can bear not only the displacements but also the rotations. The additional kinetic freedom results in four kinds of wave modes, namely, the longitudinal displacement (LD) wave, the longitudinal microrotational (LR) wave, and two coupled transverse (CT) waves. Apart from the LD wave, the other three waves are dispersive. The existence of couple stresses and the microrotations also makes the interface conditions between the micropolar slab and the classic elastic half-spaces different from that between two classic solids. The nontraditional interface conditions lead to a set of algebraic equations from which the amplitude ratios of reflection and transmission waves can be determined. Further, the energy fluxes carried by various waves are evaluated and the energy conservation is checked to validate the numerical results obtained. The influences of the micropolar elastic constants and the thickness of slab are discussed based on the numerical results. Two situations of incident P wave and incident SH wave are both considered.

Copyright © 2016 by ASME
Topics: Reflection , Waves , Slabs
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References

Figures

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Fig. 1

Wave propagation through a micropolar slab sandwiched by two elastic half-spaces

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Fig. 2

Sketch of multiple reflection and transmission waves

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Fig. 3

The dependence of the reflection and transmission coefficients upon nondimensional thickness h¯(=h/L0) in the case of incident P wave (d=0,μ¯1=0.2,λ¯2=0.2,μ¯2=0.1,ρ¯2=0.7,γ¯2=0.1,κ¯2=0.06,j¯2=1)

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Fig. 4

The dependence of energy ratios on the thickness of micropolar sandwiched layer in the case of normal incident P wave at 0.5 MHz (here, the energy ratios are modified to keep consistence with that in literature [19])

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Fig. 5

The dependence of the reflection and transmission coefficients upon the micropolar constant γ¯2 for different incident angles θPI in the case of incident P wave (d=0,μ¯1=0.75,λ¯2=0.8,μ¯2=0.6,ρ¯2=1.2,κ¯2=6,j¯2=30,h¯=0.1)

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Fig. 6

The dependence of the reflection and transmission coefficients upon the incident angle θPI for different micropolar constants γ¯2 in the case of incident P wave (d=0,μ¯1=0.75,λ¯2=0.8,μ¯2=0.6,ρ¯2=1.2,κ¯2=6,j¯2=30,h¯=0.1)

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Fig. 7

The dependence of the reflection and transmission coefficients upon the micro-inertia j¯2 for different incident angles θPI in the case of incident P wave (d=0,μ¯1=0.75,λ¯2=0.8,μ¯2=0.6,ρ¯2=1.2,γ¯2=4,κ¯2=6,h¯=0.1)

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Fig. 8

The dependence of the reflection and transmission coefficients upon the incident angle θPI for different micro-inertia j¯2 in the case of incident P wave (d=0,μ¯1=0.75,λ¯2=0.8,μ¯2=0.6,ρ¯2=1.2,γ¯2=4,κ¯2=6,h¯=0.1)

Grahic Jump Location
Fig. 9

The dependence of the reflection and transmission coefficients upon the micropolar constant κ¯2 for different incident angles θPI in the case of incident P wave (d=0,μ¯1=0.75,λ¯2=0.8,μ¯2=0.6,ρ¯2=1.2,γ¯2=4,j¯2=30,h¯=0.1)

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Fig. 10

The dependence of the reflection and transmission coefficients upon the incident angle θPI for different micropolar constant κ¯2 in the case of incident P wave (d=0,μ¯1=0.75,λ¯2=0.8,μ¯2=0.6,ρ¯2=1.2,γ¯2=4,j¯2=30,h¯=0.1)

Grahic Jump Location
Fig. 11

The dependence of the reflection and transmission coefficients upon nondimensional thickness h¯ in case of incident SH wave (d=0,μ¯1=0.2,λ¯2=0.2,μ¯2=0.1,ρ¯2=0.7,α¯2=β¯2=γ¯2=0.1,κ¯2=0.06,j¯2=1)

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Fig. 12

The dependence of reflection and transmission coefficients upon the micropolar constant γ¯2(α¯2=β¯2=γ¯2) for different incident angles θSHI in the case of incident SH wave (d=0,μ¯1=0.2,λ¯2=0.2,μ¯2=0.15,ρ¯2=0.7,κ¯2=1,j¯2=1,h¯2=0.1)

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Fig. 13

The dependence of the reflection and transmission coefficients upon the incident angle θSHI for different micropolar constants γ¯2(α¯2=β¯2=γ¯2) in the case of incident SH wave (d=0,μ¯1=0.2,λ¯2=0.2,μ¯2=0.15,ρ¯2=0.7,κ¯2=1,j¯2=1,h¯2=0.1)

Grahic Jump Location
Fig. 14

The dependence of reflection and transmission coefficients upon the micro-inertia j¯2 for different incident angle θSHI in the case of incident SH wave (d=0,μ¯1=0.2,λ¯2=0.2,μ¯2=0.15,ρ¯2=0.7,α¯2=β¯2=γ¯2=1,κ¯2=1,h¯2=0.1)

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Fig. 15

The dependence of the reflection and transmission coefficients upon the incident angle θSHI for different micro-inertia j¯2 in the case of incident SH wave (d=0,μ¯1=0.2,λ¯2=0.2,μ¯2=0.15,ρ¯2=0.7,α¯2=β¯2=γ¯2=1,κ¯2=1,h¯2=0.1)

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Fig. 16

The dependence of the reflection and transmission coefficients upon the micropolar constant κ¯2 for different incident angles θSHI in the case of incident SH wave (d=0,μ¯1=0.2,λ¯2=0.2,μ¯2=0.15,ρ¯2=0.7,α¯2=β¯2=γ¯2=1,j¯2=1,h¯2=0.1)

Grahic Jump Location
Fig. 17

The dependence of the reflection and transmission coefficients upon the incident angle θSHI for different micropolar constants κ¯2 in the case of incident SH wave (d=0,μ¯1=0.2,λ¯2=0.2,μ¯2=0.15,ρ¯2=0.7,α¯2=β¯2=γ¯2=1,j¯2=1,h¯2=0.1)

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