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IssuesArchive of Issues2013-2pp.194-202

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V.G. Popov, "Harmonic Vibrations of a Half-Space with a Surface-Breaking Crack under Conditions of Out-of-Plane Deformation," Mech. Solids. 48 (2), 194-202 (2013)
Year 2013 Volume 48 Number 2 Pages 194-202
DOI 10.3103/S0025654413020118
Title Harmonic Vibrations of a Half-Space with a Surface-Breaking Crack under Conditions of Out-of-Plane Deformation
Author(s) V.G. Popov (Odessa National Maritime Academy, Didrikhsona 8, Odessa, 65029 Ukraine, dr.vg.popov@gmail.com)
Abstract The paper presents a solution of the problem of determining the stress state in an elastic isotropic half-space with a crack intersecting its boundary under harmonic longitudinal shear vibrations. The vibrations are excited by a regular action of a harmonic shear load on the crack shores. The solution method is based on the use of the discontinuous solution of the Helmholtz equation, which allows one to reduce the original problem to a singular integro-differential equation for the unknown jump of the displacement on the crack surface. The solution of this equation is complicated by the existence of a fixed singularity of its kernel. Therefore, one of the main results is the development of an efficient approximate method for solving such equations, which takes into account the true asymptotics of the unknown function. The latter allows one to obtain a high-precision approximate formula for calculating the stress intensity factor.
Keywords crack, harmonic vibration, stress intensity factor, singular integro-differential equation, fixed singularity
References
1.  M. P. Stallybrass, "A Crack Perpendicular to an Elastic Half-Plane," Int. J. Engng Sci. 8 (5), 351-362 (1970).
2.  A. A. Khrapkov, "Certain Cases of the Elastic Equilibrium of an Infinite Wedge with a Nonsymmetric Notch at the Vertex, Subjected to Concentrated Forces," Prikl. Mat. Mekh. 35 (4), 677-689 (1971) [J. Appl. Math. Mech. (Engl. Transl.) 35 (4), 625-637 (1971)].
3.  A. A. Khrapkov, "Closed Form Solutions of Problems on the Elastic Equilibrium of an Infinite Wedge with Nonsymmetric Notch at the Apex," Prikl. Mat. Mekh. 35 (6), 1062-1069 (1972) [J. Appl. Math. Mech. (Engl. Transl.) 35 (6), 1009-1016 (1972)].
4.  L. Ya. Tikhonenko and V. A. Sitnik, "Problem of Elastic Half-Plane with a Crack Orthogonally Entering the Boundary," Dinamich. Sist., No. 4, 45-52 (1981).
5.  G. D. Gupta and F. Erdogan, "The Problem of Edge Cracks in an Infinity Strip," J. Appl. Mech. 41 (4), 1001-1005 (1974).
6.  A. P. Datsyshin, "On the Limit Equilibrium of a Half-Plane with a Surface Crack," Fiz.-Khim. Mekh. Mat. 5 (6), 746-748 (1969) [Mater. Sci. (Engl. Transl.)].
7.  V. V. Panasyuk and A. P. Datsyshin, "On the Limit Equilibrium of a Half-Plane with an Arbitrarily Oriented Crack Entering the Boundary," Fiz.-Khim. Mekhanika Mat. 7 (6), 102-104 (1971) [Mater. Sci. (Engl. Transl.)].
8.  M. P. Savruk, Two-Dimensional Problems of Elasticity for Bodies with Cracks (Naukova Dumka, Kiev, 1981) [in Russian].
9.  I. N. Sneddon and S. C. Das, "The Stress Intensity Factor at the Tip of an Edge Crack in an Elastic Half-Plane," Int. J. Engng Sci. 9 (1), 25-35 (1971).
10.  Y. Z. Chen and N. Hasele, "Solution of Multiple-Edge Crack Problem of Elastic Half-Plane by Using Singular Integral Equation Approach," Commun. Numer. Methods Engng 11 (7), 607-611 (1995).
11.  S. W. Liu, J. C. Sung, and S. S. Chang, "Transient Scattering of SH Waves by Surface-Breaking and Subsurface Cracks," Int. J. Solids Struct. 34 (30), 4019-4035 (1997).
12.  D. A. Mendelson, I. D. Achenbach, and L. M. Keer, "Scattering at Elastic Waves by a Surface-Breaking Crack," Wave Motion 2 (3), 277-292 (1980).
13.  I. D. Achenbach and R. J. Brind, "Scattering of Surface Waves by a Sub-Surface Crack," J. Sound Vibr. 76 (1), 43-56 (1981).
14.  C. Zhang and I. D. Achenbach, "Numerical Analysis of Surface Wave Scattering by the Boundary Element Method," Wave Motion 10 (4), 365-374 (1988).
15.  P. S. Dineva, G. D. Manolis, and T. V. Rangelov, "Sub-Surface Crack in an Inhomogeneous Half-Plane. Wave Scattering Phenomena by BEM," Engng Anal. Boundary Elem. 30 (5), 350-362 (2006).
16.  Ch. Zhang, "Dynamic Stress Intensity Factors of an Inclined Surface-Breaking Crack," Ehgng Frac. Mech. 37 (1), 7-14 (1990).
17.  Y. S. Angel, "Reflection and Transmission of Antiplane Surface by a Surface-Breaking Crack in a Layered Elastic Solid," Wave Motion 20 (4), 371-383 (1994).
18.  V. G. Popov, "Studies of Stress and Displacement Fields in Diffraction of Elastic Shear Waves at a Thin Rigid Separated Inclusion," Izv. Akad. Nauk. Mekh. Tverd. Tela, No. 3, 139-146 (1992) [Mech. Solids (Engl. Transl.)].
19.  R. V. Duduchava, "Integral Equations of Convolution with Discontinuous Presymbols, Singular Integral Equations with Fixed Singularities, and Their Applications to Problems of Mechanics," in Proc. Tbilisi Math. Institute, Acad. Sci. USSR, Vol. 60 (1979), pp. 3-135 [in Russian].
20.  A. R. Andreev, "Direct Numerical Method for Solving Singular Integral Equations of the First Kind with Generalized Kernels," Izv. Akad. Nauk. Mekh. Tverd. Tela, No. 1, 126-146 (2005) [Mech. Solids (Engl. Transl.) 40 (1), 104-119 (2005)].
21.  V. I. Krylov, Approximate Computations of Integrals (Nauka, Moscow, 1967) [in Russian].
22.  G. Szegö, Orthogonal Polynomials (Amer. Math. Soc, Providence, 1959; Fizmatgiz, Moscow, 1962).
23.  V. G. Popov, Concentration of Elastic Stresses Near Stamps, Cuts, Thin Inclusions, and Reinforcements (Nauka, Moscow, 1982) [in Russian].
24.  I. S. Gradshtein and I. M. Ryzhik, Tables of Integrals, Sums, Series, and Products (Nauka, Moscow, 1971) [in Russian].
25.  A. P. Prudnikov, Yu. A. Brychkov, and O. I. Marichev, Integrals and Series: Special Functions (Nauka, Moscow, 1983) [in Russian].
Received 03 June 2010
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