scholarly journals Interaction between rigid-disc inclusion and penny-shaped crack under elastic time-harmonic wave incidence

2009 ◽  
Vol 46 (3-4) ◽  
pp. 602-616 ◽  
Author(s):  
V.V. Mykhas’kiv ◽  
O.M. Khay
Keyword(s):  
Harmonic Wave ◽  
Time Harmonic ◽  
Penny Shaped Crack ◽  
Shaped Crack ◽  
Rigid Disc ◽  
Wave Incidence

Diffraction of elastic waves by a penny-shaped crack

1981 ◽  
Vol 378 (1773) ◽  
pp. 263-285 ◽  
Keyword(s):  
Integral Equation ◽  
Boundary Value Problem ◽  
Unique Solution ◽  
Double Layer ◽  
Elastic Waves ◽  
Boundary Value ◽  
Elastic Solid ◽  
Time Harmonic ◽  
Penny Shaped Crack ◽  
Shaped Crack

Consider an infinite elastic solid containing a penny-shaped crack. We suppose that time-harmonic elastic waves are incident on the crack and are required to determine the scattered displacement field u i . In this paper, we describe a new method for solving the corresponding linear boundary-value problem for u i , which we denote by S. We begin by defining an ‘elastic double layer’; we prove that any solution of S can be represented by an elastic double layer whose ‘density’ satisfies certain conditions. We then introduce various Green functions and define a new crack Green function, G ij , that is discontinuous across the crack. Next, we use G ij to derive a Fredholm integral equation of the second kind for the discontinuity in u i across the crack. We prove that this equation always has a unique solution. Hence, we are able to prove that the original boundary-value problem S always possesses a unique solution, and that this solution has an integral representation as an elastic double layer whose density solves an integral equation of the second kind.

Bi-material transversely isotropic half-space containing penny-shaped crack under time-harmonic horizontal loads

2017 ◽  
Vol 172 ◽  
pp. 152-180 ◽  
Author(s):  
Morteza Eskandari-Ghadi ◽  
Azizollah Ardeshir-Behrestaghi ◽  
Ronald Y.S. Pak
Keyword(s):  
Half Space ◽  
Transversely Isotropic ◽  
Time Harmonic ◽  
Penny Shaped Crack ◽  
Shaped Crack

Scattering by a horizontal subsurface penny-shaped crack

1986 ◽  
Vol 408 (1835) ◽  
pp. 277-294 ◽  
Keyword(s):  
Crack Opening ◽  
Resonance Phenomenon ◽  
Polar Coordinates ◽  
Axially Symmetric ◽  
Opening Displacement ◽  
Time Harmonic ◽  
Wave Resonance ◽  
Penny Shaped Crack ◽  
Rectangular Coordinates ◽  
Shaped Crack

The scattering by a horizontal subsurface penny-shaped crack subjected to axially symmetric loading is investigated. The formulation begins with deriving the response of a time harmonic point force in rectangular coordinates. Then, the integral representation and integral equations are converted into polar coordinates by applying the condition of axial symmetry. The results contain crack opening displacement (COD), stress intensity factors, scattered pattern and the frequency spectrum of the Rayleigh wave and the back-scattered longitudinal wave. Resonance phenomenon is compared with the plane strain case solved in an earlier paper.

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