Diffraction of elastic waves on an inclined crack in a layer. (Russian) Zbl 1164.74053
The authors discuss a problem of diffraction of normal waves on an inclined crack in an elastic layer. Integral equation is derived with an explicit representation of the Fourier symbol of kernel in the form of matrix product. The influence of the crack inclination angle on the effects of resonant capture and wave energy localization for the case of horizontal crack is analyzed.
Reviewer: V. P. Phil’chakova (Kyïv)
MSC:
| 74A45 | Theories of fracture and damage |
| 74J99 | Waves in solid mechanics |
| 74H45 | Vibrations in dynamical problems in solid mechanics |
References:
| [1] | Boström, A.: Review of hypersingular integral equation method for crack scattering and application to modeling of ultrasonic nondestructive evaluation. Appl mech rev 56, No. 4, 383-405 (2003) |
| [2] | Van Der Hijden, J. H. M.T.; Neerhoff, F. L.: Diffraction of elastic waves by a sub-surface crack (in-plane motion). J acoust soc am 75, No. 6, 1694-1704 (1984) · Zbl 0538.73029 |
| [3] | Vatul’yan, A. O.: Boundary integral equations of the first kind in dynamic problems of the anisotropic theory of elasticity. Dokl ross akad nauk 333, No. 3, 312-314 (1993) · Zbl 0826.73008 |
| [4] | Glushkov, Ye.V.; Glushkova, N. V.; Shapar’, Ye.M.: Blocking of a Rayleigh wave by a near-surface crack. Dokl ross akad nauk 398, No. 6, 764-770 (2004) |
| [5] | Glushkov, Ye.V.; Glushkova, N. V.; Golub, M. V.: Blocking of travelling waves and localization of the energy of elastic vibrations in diffraction by a crack. Akust zhurnal 52, No. 3, 314-325 (2006) |
| [6] | Glushkov, E.; Glushkova, N.; Golub, M.; Boström, A.: Natural resonance frequencies, wave blocking, and energy localization in an elastic half-space and waveguide with a crack. J acoust soc am 119, No. 6, 3589-3598 (2006) |
| [7] | Babeshko, V. A.; Glushkov, Ye.V.; Zinchenko, Zh.F.: Dynamics of inhomogeneous linear elastic media. (1989) · Zbl 0698.73016 |
| [8] | Glushkov, E.; Glushkova, N.; Ekhlakov, A.; Shapar, E.: An analytically based computer model for surface measurements in ultrasonic crack detection. Wave motion 43, No. 6, 458-473 (2006) · Zbl 1231.74238 |
| [9] | Lifanov, I. K.: The method of singular integral equations and numerical experiment (in mathematical physics, aerodynamics, the theory of elasticity, and wave diffraction). (1995) · Zbl 0904.73001 |
| [10] | Aleksandrov, V. M.; Smetanin, B. I.; Sobol’, B. V.: Thin stress concentrators in elastic bodies. (1993) · Zbl 0805.73013 |
| [11] | Popov, G. Ya.: Concentration of elastic stresses near punches, cuts, thin inclusions, and reinforcements. (1980) |
| [12] | Krenk, S.; Schmidt, H.: Elastic wave scattering by a circular crack. Phil trans roy soc London 308, No. 1502, 167-198 (1982) · Zbl 0523.73018 |
| [13] | Prudnikov, A. P.; Brychkov, Yu.A.; Marichev, O. I.: Integrals and series. Special functions. (1983) · Zbl 0626.00033 |
| [14] | Liu, G. R.: A combined finite element/strip element method for analyzing elastic wave scattering by cracks and inclusions in laminates. Comput mech 28, 76-81 (2002) · Zbl 1115.74370 |
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