Scattering of SH wave by a crack terminating at the interface of a bimaterial (original) (raw)
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Scattering and diffraction of SH waves by a finite crack: an analytical solution
Geophysical Journal International, 2001
The diffraction of SH waves by a finite plane crack is studied. The classical Sommerfeld solution for a semi-infinite straight reflecting screen is used as a building block to calculate the diffracted field generated by a finite crack. The solution is derived from the analysis of the behaviour of diffracted waves. These waves, which are first generated at the edges of the crack, travel along the surfaces and are diffracted/reflected at the opposite edge. By iteratively taking into account the contribution to the total field of these travelling waves, an infinite series with a known limit is constructed, leading to an approximate analytical solution for the case of a finite plane crack. This solution is virtually exact for large frequencies and it is very good for incoming wavelengths of up to four times the size of the crack. Since the solution is explicit the computational cost is very low. Both frequency and time-domain results are included.
The scattering of SH waves by a finite crack with a superposition-based diffraction technique
Studia Geophysica et Geodaetica, 2016
The problem of diffraction of cylindrical and plane SH waves by a finite crack is revisited. We construct an approximate solution by the addition of independent diffracted terms. We start with the derivation of the fundamental case of a semi-infinite crack obtained as a degenerate case of generalized wedge. This building block is then used to compute the diffraction of the main incident waves. The interaction between the opposite edges of the crack is then considered one term at a time until a desired tolerance is reached. We propose a recipe to determine the number of required interactions as a function of frequency. The solution derived with the superposition technique can be applied at low and high frequencies.
Journal of theoretical and applied mechanics, 2016
Elastic wave scattering by cracks at macro-and nano-scale in anisotropic plane under conditions of plane strain is studied in this work. Furthermore, time-harmonic loads due to incident plane longitudinal P-or shear SV-wave are assumed to hold. In a subsequent step, the elastodynamic fundamental solution for general anisotropic continua derived in closed-form via the Radon transform is implemented in a numerical scheme based on the traction boundary integral equation method (BIEM). The surface elasticity effect in the case of nano-crack is taken into consideration via non-classical boundary condition along the crack surface proposed by Gurtin and Murdoch [1]. The numerical results obtained herein reveal substantial differences between anisotropic materials containing a macro-and a nano-crack in terms of their dynamic stress response, where the latter case demonstrates clearly the strong influence of the size-effects. Finally, these types of examples serve to illustrate the present approach and to show its potential for evaluating the stress concentration fields (SCF) inside cracked nanocomposites. The obtained results concern the reliability and safety of the advancing nanomaterials.
Journal of Computational Mathematics, 2010
The wave scattering problem by a crack Γ in R 2 with impedance type boundary is considered. This problem models the diffraction of waves by thin two-sided cylindrical screens. A numerical method for solving the problem is developed. The solution of the problem is represented in the form of the combined angular potential and single-layer potential. The linear integral equations satisfied by the density functions are derived for general parameterized arcs. The weakly singular integrals and the Cauchy singular integral arising in these equations are computed using a highly accurate scheme with a truncation error analysis. The advantage of the scheme proposed in this paper is, in one hand, the fact that we do not need the analytic property of the crack and we allow different complex valued surface impedances in both sides of the crack. In the other hand, we avoid the hyper-singular integrals. Numerical implementations showing the validity of the scheme are presented.
Numerical simulation of multiple scattering of P and SV waves caused by near-surface parallel cracks
Geofísica Internacional, 2016
Scattering and diffraction of P and SV waves caused by parallel oriented cracks located near to a free surface are investigated in this work. The Indirect Boundary Element Method (IBEM) was applied for studying the wave propagation phenomena in a half-plane model that contain the cracks. Various incidence angles of P and SV waves are considered. Sometime before it has been reported that a near free-surface crack generates scattered surface waves whose amplitude spectra show conspicuous resonance peaks. Such effect has been attributed to local resonances originated in a virtual layer between the shallowest crack and the free surface. For our case of two parallel crack system, where cracks are located at different depths, the amplitude spectra show additional peaks, which can be associated with the presence of the second crack. Given similar sizes between these two cracks, the characteristic resonance frequency observed at the free surface corresponds mainly to the equivalent layer fo...
Scattering By Cracks: Numerical Simulations Using A Boundary Finite Element Method
2002
feature of the far field pattern of the scattered wave. show that even with sparse meshes the method is able to give a global where it becomes clear the good convergence of the method. Moreover, we non planar cracks in the three dimensional case, presenting several examples information on the shape of the scattering obstacle. We include the case of potential. Simulations on the far field patterns allow to characterize some method applied to a variational formulation derived from the double layer in the resonance region. The results are obtained with a boundary element We present several simulations of the amplitude scattered by acoustic cracks 1 Introduction mainly penny-shaped flat cracks. non hypersingular kernel. First attempts considered only simple geometries, express the exterior domain problem in terms of an integral equation with a tried to solve this problem. In terms of integral equations, the difficultyis to materials. Early works by Bouwkamp[5]and Jones[S],in the acoustic case, plications in industrial problems, for instance, the detection of cracks in Acoustic and elastic scattering by cracks is an old issue, with many a p
Scattering of elastic waves by a 2-D crack using the Indirect Boundary Element Method (IBEM)
Geophysical Journal International, 2005
The scattering of elastic waves by cracks is an old problem and various ways to solve it have been proposed in the last decades. One approach is using dual integral equations, another useful and common formulation is the Boundary Element Method (BEM). With the last one, the boundary conditions of the crack lead to hyper-singularities and particular care should be taken to regularize and solve the resulting integral equations.