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TECHNICAL PAPERS

On Scattering in a Piezoelectric Medium by a Conducting Crack

[+] Author and Article Information
Shaofan Li1

Department of Civil and Environmental Engineering, University of California, Berkeley, CA 94720li@ce.Berkeley.edu

Albert C. To, Steven D. Glaser

Department of Civil and Environmental Engineering, University of California, Berkeley, CA 94720

1

To whom correspondence should be addressed.

J. Appl. Mech 72(6), 943-954 (Apr 09, 2005) (12 pages) doi:10.1115/1.2047627 History: Received December 25, 2004; Revised April 09, 2005

The work is concerned with the characterization of a Kirchhoff diffraction field in a piezoelectric material. An exact solution is obtained for the full scattering fields around the tip of a semi-infinite crack, which is electrically conducting and is loaded with both SH acoustic incident waves and in-plane electrical incident waves. First, it is found that a conducting crack in a piezoelectric solid is not completely opaque to the electro-acoustic wave, i.e., the electro-acoustic wave can penetrate and transmit to the other side of the crack surface. Second, the analysis has confirmed that the interaction between electrical wave and acoustic wave will provide multiple electrical and electro-acoustic head waves. Third, by solving the problem, we have established a rigorous electro-acoustic scattering theory in piezoelectric/ferroelectric media, which is different from the scattering theory in purely elastic media. The characterization of the scattering fields in piezoelectric media provides a unique signature database for electro-acoustic waves in piezoelectric materials.

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Copyright © 2005 by American Society of Mechanical Engineers
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References

Figures

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Figure 6

The scattering patterns excited by an electric source

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Figure 8

Displacement time histories at various θ with fixed y due to an impulsive electric source incident at θℓ=45°. Labels: i=incident wave, h=head wave, and s=scattered wave.

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Figure 1

Schematic illustration of a system of plane waves due to an incident acoustic wave approaching a semi-infinite crack

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Figure 2

The Cagniard-deHoop inversion paths Γα, Γβ, and Γαβ for acoustic excitation

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Figure 3

The scattering patterns excited by an acoustic source: case (1)

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Figure 4

The scattering patterns excited by an acoustic source: case (2)

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Figure 5

The Cagniard-deHoop inversion paths for pseudo-electric excitation

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Figure 9

Amplitude of the normalized stress phase function for various electro-mechanical coupling coefficients (k̃e) (a) versus incident angle for an incident acoustic source Gσ∕w0 and (b) versus incident angle for an incident electric source Gσ∕ψ0

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Figure 10

Amplitude of the normalized electric displacement phase function for various electro-mechanical coupling coefficients (k̃e) (a) versus an incident acoustic source GD∕w0 and (b) versus an incident electric source GD∕ψ0

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Figure 11

Amplitude of the normalized electric field phase function for various electro-mechanical coupling coefficients (k̃e) (a) versus an incident acoustic source GE∕w0 and (b) versus an incident electric source GE∕ψ0

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Figure 7

Displacement-time histories at various θ with fixed y due to an impulsive acoustic source incident at θa=45°. Labels: i=incident wave, h=head wave, and s=scattered wave.

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