Diffraction of horizontal shear waves by a moving interface crack

Summary An analysis of the diffraction of horizontally polarized shear waves by a finite crack moving on a bimaterial interface is carried out. Fourier transform method is used to reduce the mixed boundary value problem to the solutions of two pairs of dual integral equations. These equations are further reduced to a pair of Fredholm integral equations of the second kind. The dynamic stress intensity factors are obtained for several values of wave number, incident angle, crack velocity, and material constants.With 7 Figures     

Diffraction of transient horizontal shear waves by a finite crack at the interface of two bonded dissimilar elastic solids

Scattering of transient horizontal shear waves by a finite crack located at the interface of two bonded dissimilar elastic solids is investigated in this study. Laplace and Fourier transform technique is used to reduce the problem to a pair of dual integral equations. The solution of the dual integral equation is expressed in terms of the Fredholm integral equation of the second kind having the kernel of a finite integration. Dynamic stress intensity factor is obtained as a function of the material and geometric properties and time.     

Diffraction of shear waves by an edge crack in an elastic wedge

Low frequency diffraction of plane harmonic shear (SH) wave by an edge crack in an elastic wedge of arbitrary vertex angle is studied. Kontorowich-Lebedev transform is used to solve the mixed boundary value problem under consideration. For low frequency case, i.e. wavelength large compared to the length of the crack, the displacement field is obtained by successive approximation of the resulting Wiener-Hopf equation. For the limiting case of an elastic half space the results agree with those obtained by the method of matched asymptotic expansions.     

Diffraction of SH waves by a moving crack

Summary The problem of diffraction of anti-plane shear waves by a running crack of finite length is investigated analytically. Fourier transform method is used to solve the mixed boundary value problem which reduces to two pairs of dual integral equations. These dual integral equations are further reduced to a pair of Fredholm integral equations of the second kind. The iterative solution of the integral equations has been obtained for small wave number. The solution is used to calculate the dynamic stress intensity factor at the edge of the crack.With 2 Figures     

Diffraction of high frequency torsion waves by a penny-shaped crack

The diffraction of high frequency torsion waves by a penny-shaped crack situated in an infinite isotropic elastic solid is considered. Asymptotic expressions for the dynamic stress intensity factors are derived for a variety of incident excitations, and the results predict an oscillatory behaviour of these factors at high frequencies.     

Diffraction of elastic waves by an elliptic crack

The integral equation method is used to obtain the scattered field of a normally incident plane wave from an elliptic crack embedded in an isotropic elastic medium. It is shown that the determination of the diffracted field depends on the solution of integro-differential equation. A formal power series solution, in the low frequency limit, is obtained. Expressions are derived for the scattered amplitudes and the dynamic stress intensity factor.     

Diffraction of water waves by a moored,horizontal, flat plate

Summary A Norwegian research group has investigated the feasibility of constructing a system of underwater structures which would act like a lens and focus water waves prior to harnessing their energy. In the present work we consider modelling one of these structures by a horizontal, flat plate which is moored to the seabed. The water is assumed to be incompressible and inviscid and two-dimensional, linear, irrotational theory is used. Solutions to the scattering and radiation potentials are obtained by the method of matched eigenfunction expansions. Comparisons are made with various approximate solutions and results are presented illustrating the effect of varying the mooring stiffness in the cables on both the responses of the plate and the far-field wave motion.     

Diffraction of anti-plane shear waves by two moving griffith cracks

The problem of diffraction of anti-plane shear waves by two running Griffith cracks of finite length is investigated by using the Fourier transform method. The mixed boundary value problem is reduced to a pair of triple integral equations having trigonometrical kernels. Using the finite Hilbert transform technique, a solution of the pair of triple integral equations is obtained for the small wave number. Approximate formulae are derived for the stress intensity factors. Numerical results for the stress intensity factors are displayed vs wave number for different crack lengths, velocities and angles of incidence.     

Diffraction of shear waves by a rigid strip in a medium of monoclinic type

Summary The paper discusses the two dimensional problem of diffraction of shear waves by a rigid strip in an infinite medium of monoclinic type. This problem is reduced to a system of dual integral equations of which the solution provides the diffracted field. The method of steepest descent has been used in the determination of the diffracted fields at a large distance from the strip. Diffraction pattern for displacement and stress field have been computed and the effect of anisotropy is distinctly marked.With 6 Figures     

Scattering of antiplane shear waves by a finite crack in piezoelectric laminates

Summary Following the dynamic theory of linear piezoelectricity, we consider the scattering of horizontally polarized shear waves by a finite crack in a composite laminate containing a piezoelectric layer. The piezoelectric layer is bonded between two half-spaces of a different elastic solid. The crack is normal to the interfaces and is placed at an equal distance away from them. Both cases of a partially broken layer and a completely broken layer are studied. Fourier transforms are used to reduce the problem to the solution of a pair of dual integral equations. The solution of the dual integral equations is then expressed in terms of a singular integral equation. The propagation of symmetric first mode is studied numerically, and the dynamic stress intensity factor and the dynamic energy release rate are obtained for some piezoelectric laminates.     

Diffraction of long waves by a step

Summary The problem of diffraction of long water waves by a step is considered. First a functional equation in the Fourier transform domain is derived, which is of the generalised form, and its solution is expressed in terms of constants satisfying an infinite set of linear algebraic equations. Next, the final solution for the far field is obtained asymptotically; this solution also concerns the corresponding problems in acoustics and electromagnetism.With 2 Figures     

Mass sensitivities of shear horizontal waves in three-layer platesensors

Explicit velocity and mass sensitivity formulas for shear-horizontal (SH) plate wave sensors loaded symmetrically on both sides of a plate are presented. The sensor geometry is a composite plate which consists of a central isotropic plate sandwiched symmetrically between two identical layers of isotropic solids. It is demonstrated that if the side layers are considered as the mass loading, for the lowest SH mode (SSo) the sensitivity decreases by a factor of (1-(μ ₂/ρ₂)/(μ₁/ρ₁)) due to the elasticity and by a factor of (1+ρ₂h/ρ₁d)^-1 due to the inertia of the mass loading layers, where μ₁,μ₂ ; ρ₁, ρ₂ and 2d, h are the shear moduli, densities and thickness of the central plate and of the side layers, respectively. For higher order modes, the behavior of sensors which are operated near cutoff frequency is analyzed. The mass loading decreases the cutoff frequencies of the higher order modes and near the cutoff frequencies the mass sensitivities are very high but decrease dramatically as the mass loading increases. Specific examples are given for the case of a fused silica plate sandwiched between two thin lucite layers     

Propagation of a transient shear wave from a crack in an elastic plate

A simple analytical technique based on the methods of transverse resonance and group velocity is developed in order to predict the propagation of shear (SH) waves emitted from a crack in elastic plates. Since a total solution of the Rayleight Lamb waves propagation inside the plate is very complicated, the simple SH mode was used to demonstrate the argument of this paper. The effects of varying distances between the crack and the sensor are also discussed.

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Résumé On développe une technique analytique simple basée sur les procédés de résonance transversale et de vitesse de trains d'onde en vue de prédire la propagation d'ondes SH émises à partir d'une fissure dans une plaque élastique.Comme une solution complète pour la propagation des ondes de Rayleight-Lamb est très compliquée à mettre en oeuvre, on s'est restreint à utiliser le mode SH pour démontrer la validité de l'étude.On discute également des effets d'une distance variable entre la fissure et le palpeur.

     

Scattering of the harmonic anti-plane shear waves by a crack in functionally graded piezoelectric materials

In the present paper, the dynamic behavior of a Griffth crack in the functionally graded piezoelectric material (FGPM) is investigated. It is assumed that the elastic stiffness, piezoelectric constant, dielectric permittivity and mass density of the FGPM vary continuously as an exponential function, and that FGPM is under the anti-plane mechanical loading and in-plane electrical loading. By using the Fourier transform and defining the jumps of displacement and electric potential components across the crack surface as the unknown functions, two pairs of dual integral equations are derived. To solve the dual integral equations, the jumps of the displacement and electric potential components across the crack surface are expanded in a series of Jacobi polynomial. Numerical examples are provided to show the effects of material properties on the stress and the electric displacement intensity factors.     

Diffraction of normal compression waves by a penny-shaped crack in the presence of an axial magnetic field

The problem of diffraction of normally incident compressional waves by a penny-shaped crack located in a perfectly conducting, infinite, isotropic, elastic solid permeated by an uniform magnetostatic field is considered. Using an integral transform technique, the problem is reduced to that of solving a Fredholm integral equation of the second kind having a finite integral kernel. The dynamic singular stress distributions near the crack tip are obtained in closed form and the effects on the dynamic stress-intensity factors due to the presence of the magnetic field are shown graphically. For low frequencies, the dynamic stress-intensity factors are expressed in series of ascending powers of the normalized frequency. The approximate solutions are compared with exact solutions.     

Propagation of a crack due to shear waves in a medium of monoclinic type

Summary In this paper the propagation of a crack due to shear waves in a medium having monoclinic symmetry is investigated. The stress intensity factor at the crack tip for concentrated force of a constant intensity and for constant loading is separately calculated. The Wiener-Hopf technique has been used to solve the problem. It has been shown that the stress intensity factor decreases as the length of the crack increases. The effect of anisotropy being distinctly marked.With 5 Figures     

Diffraction of torsional waves by a flat annular crack at the interface of two bonded dissimilar elastic solids

The paper deals with the problem of finding the stress distribution near an annular crack located at the interface of two bonded dissimilar elastic solids. The crack is opened by the interaction of a torsional wave incident normally on the annular crack. The problem is reduced to the solution of three simultaneous Fredholm integral equations. The numerical solution of these simultaneous integral equations has been obtained. The solution is used to calculate the stress-intensity factors at the tips of the crack.     

Diffraction of torsional waves by a penny-shaped crack in an infinitely long cylinder bonded to an infinite medium

This paper contains an analysis of the interaction of torsional waves with penny-shaped crack located in an infinitely long cylinder which is bonded to an infinite medium. Both the cylinder and infinite medium are of homogeneous and elastic but dissimilar materials. The solution of the problem is reduced to a Fredholm integral equation of the second kind which is solved numerically. The numerical solution is used to calculate the stress intensity factor at the rim of the penny-shaped crack.