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Research Papers

Two-Dimensional Elastodynamic Scattering by a Finite Flat Crack

[+] Author and Article Information
V. F. Emets

Professor
Institute of Information Technology,
Lodz University of Technology,
Wolczanska 215,
Lodz 93-005, Poland
e-mail: volodymyr.yemyets@p.lodz.pl

J. Rogowski

Assistant Professor
Institute of Information Technology,
Lodz University of Technology,
Wolczanska 215,
Lodz 93-005, Poland
e-mail: jan.rogowski@p.lodz.pl

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received January 19, 2016; final manuscript received February 4, 2016; published online February 22, 2016. Editor: Yonggang Huang.

J. Appl. Mech 83(5), 051004 (Feb 22, 2016) (5 pages) Paper No: JAM-16-1032; doi: 10.1115/1.4032691 History: Received January 19, 2016; Revised February 04, 2016

The diffraction of elastic harmonic waves by a finite plane tunnel crack is studied. A solution is derived from an analysis of the integral equations describing the problem, using the Wiener–Hopf technique and the method of compound asymptotic expansions. Taking into account the successive reflections of Rayleigh waves from crack tips, an approximate analytical solution is expressed in a closed-form that is computationally effective and yields accurate results in the resonance region of dimensionless wave numbers. Both direct and inverse scattering problems are considered.

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References

Figures

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Fig. 1

Geometry of the problem

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Fig. 2

Integration contour Γ in a complex plane

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Fig. 3

Deformed contour Γ in the lower half-plane

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Fig. 4

Normalized plane wave scattering cross section for two angles of incidence: θ0=0 (top) and θ0=π/2 (bottom)

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