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Non destructive examination of industrial structures requires the modeling of specimen geometry echoes generated by the surfaces (entry, back-wall, etc.) of inspected blocks. For that purpose, the study of plane elastic wave diffraction by a wedge is of great interest since surfaces of complex industrial specimen often include dihedral corners. These inspections often deal with high frequency (f = 2–5 MHz) ultrasonic waves. Simulation of realistic inspections by finite elements and finite differences can therefore be time consuming because such methods require a small mesh step for a better description of the scattered wave. Semi-analytical methods are therefore preferred for high frequency problems. There exist various approaches for semi-analytical modeling of plane elastic wave diffraction by a wedge but the theoretical and numerical aspects of these methods have so far only been developed for wedge angles lower than π. Croisille and Lebeau [1] have introduced a resolution method called the Spectral Functions method in the different case of an immersed elastic wedge of angle less than π. Kamotski and Lebeau [2] have then proven existence and uniqueness of the solution derived from this method to the diffraction problem of stress-free wedges embedded in an elastic medium. The advantages of this method are its validity for wedge angles greater than π and its adaptability to more complex cases. The methodology of Croisille and Lebeau [1] has been first extended by the authors to the simpler case of an immersed soft wedge [3] (submitted). It has then been developed here for the 2D scattering problem of an elastic longitudinal wave and a numerical validation of the method for all wedge angles is proposed.
The radiation and diffraction of steady-state elastic waves in a periodically perforated orthotropic plane
The radiation and diffraction of steady-state elastic waves in a periodically perforated orthotropic plane
72D elastic plane-wave diffraction by a stress-free wedge of arbitrary angle
2D elastic plane-wave diffraction by a stress-free wedge of arbitrary angle
1On the theory of diffraction of cylindrical elastic waves and weak shock waves
On the theory of diffraction of cylindrical elastic waves and weak shock waves
42Scattering of Elastic Waves by a Plane Crack of Finite Width
A rigorous theory of the diffraction of time-harmonic elastic waves by a cylindrical, stress-free crack embedded in an elastic medium is presented. The incident wave is taken to be either a P-wave or an SV-wave. The resulting boundary-layer problem for the unknown jump in the particle displacement across the crack is solved by employing an integral-equation approach. The jump is expanded in a complete sequence of Chebyshev polynomials, and, writing the Green’s function as a Fourier integral, a system of algebraic equations is obtained. Numerical results are presented in the form of dynamic stress intensity factors, scattering cross sections, and normalized power-scattering characteristics. Some of them deviate from earlier published results.
Read more3Diffraction of elastic waves by a rigid 90° wedge Part II
Integrals representing the reflected and diffracted elastic waves generated by the incidence of a plane compressional wave on a rigid quarter-plane are evaluated by an application of the Cagniard-De Hoop technique. It is shown that diffracted spherical waves radiate away from the tip of the quarter-plane at the shear and compressional wave speeds. The spherically spreading compressional wave excites secondary shear waves on the surfaces and edges of the quarter-plane. These secondary spherical wavelets envelope a ruled surface which is conical in shape at the edges of the scatterer. The envelope propagates away from the quarter-plane at the critical angle and forms a Mach wave or bow wave. The usual reflected shear and compressional plane waves are also present and combine with the diffracted waves to form the geometric shadow of the quarter-plane.
Read moreScattering on a Small Inhomogeneity in an Elastic Medium
Problems on the diffraction of elastic plane waves (transverse and longitudinal) scattered on a cylinder are investigated. The radius a of the cylinder is small enough (\(ka \ll 1\), where \(k\) is the wave number). The waves of horizontal polarization (SH waves) are scattered similarly to the electromagnetic wave of the respective polarization. It is proved that a small inhomogeneity radiates as a point source, with its amplitude proportional to the difference of the Lame parameters \(\mu _1\) and \(\mu _2\) and to the area of a cross section of the inhomogeneity. The scattering of a plane wave of vertical polarization is subject to a more complicated law of radiation, because of the vector nature of the problem, and the respective components of the displacement vector are represented in terms of the scalar and vector potentials. However, the scattering of the wave field on the small inhomogeneity has qualitatively the same asymptotic behavior as in the case of the SH wave. Bibliography: 4 titles.
Read more46A derivation of the seismic representation theorem using seismic reciprocity
The seismic representation theorem is very useful in determining seismic displacements: (1) from extended and moving sources; (2) for boundary-value problems; and (3) for diffraction by vanishingly thin screens. Derivations of the representation theorem for anisotropic and homogeneous elastic media have been given by Knopoff [1956] and deHoop [1958] starting from first principles. These derivations, while elegant, are difficult. The seismic representation theorem is derived in a simple straightforward manner using the principle of seismic reciprocity as the starting point. The derivation is simplified further by the use of the polyadic notation. The representation theorem obtained is valid for anisotropic, inhomogeneous, linear elastic media. The utility of the representation theorem is demonstrated by considering illustrative examples concerning: (1) the radiation fields from various force couples; (2) the radiation from moving forces; and (3) the diffraction of elastic waves by thin screens.
Read more10Diffraction of elastic waves by a rigid 90° wedge Part I
The problem of calculating the reflected and diffracted elastic waves generated when a plane compressional wave strikes a rigid quarter plane is formulated as a Wiener-Hopf problem in two complex variables. It is shown how a closed form solution of this two variable Wiener-Hopf problem can be obtained provided that the Laplace transform of the elastic wave Green's function can be factorized into factors having suitable analytic properties.
Read more1The computational efficiency of a spectral walsh function method
The computational efficiency of a spectral walsh function method
Comparison of displacement and stress fields upon diffraction of elastic waves at different defects: Cracks and thin rigid intrusions
This paper considers the problem of diffraction of elastic waves at rectilinear defects (cracks or thin rigid intrusions) in an unbounded elastic medium. A discontinuous solution of the Helmholtz equation is used to reduce the problem to a singular integral equation in unknown jumps. There is a detailed analysis and comparison of the stressed state close to the defects and the diffraction field at large distances from the defect for defects of different types.
Read more26Diffraction of elastic waves by cracks or cavities using the discrete wavenumber method
A new method to calculate the diffraction of elastic waves by cracks or cavities is presented. The method yields the complete diffracted wave field and is valid at any frequency. It is based on a discretization of the inclusion surface and on the assumption of a periodic repetition of the diffracting inclusion. Body forces are applied at the discretized points along the inclusion surface and the discrete wavenumber method is used to evaluate the resulting radiation. The application of the boundary conditions then leads to a linear system of equations, which is solved by matrix inversion. Examples of calculation and comparisons with results from other techniques are presented in the case of plane incident waves as well as in the case of a line source. The presence of a free surface is also considered.
Read more2Diffraction of elastic waves in the plane multiply-connected region and dynamic stress concentration
Diffraction of elastic waves in the plane multiply-connected region and dynamic stress concentration
20Diffraction of elastic waves by two coplanar and parallel rigid strips
Diffraction of elastic waves by two coplanar and parallel rigid strips
5Maser Amplification of 9.5-Gigahertz Elastic Waves in Sapphire Doped with Divalent Nickel Impurity Ions
The three spin energy levels of divalent nickel impurity ions in sapphire interact strongly with ultrasonic waves whose frequency corresponds to certain allowed transitions between the levels. Under population inversion of the levels it is possible to achieve significant amplification of very high frequency ultrasonic waves by stimulated emission from the spin system.
Read more1Conference on developments in wave propagation: Introduction
In connection with its Industrial Associates program, the California Institute of Technology sponsors four or five conferences or symposia each year on scientific subject matter of topical interest. In May 1961 the Division of Engineering at Caltech was host to a conference on ‘Developments in Wave Propagation’ in this continuing program. With wave propagation as a common theme, the conference program drew on recognized authorities from a broad variety of physical fields for modern accounts of the knowledge, existing problems, and techniques for dealing with them. Specifically, the 3-day meeting had twelve 1-hour lectures, given in sessions on Methods in Wave Problems, Diffraction and Scattering of Elastic Waves, Waves in Dispersive Elastic and Anelastic Media, Hydrodynamic and Magnetohydrodynamic Waves, Electromagnetic Waves, and Nuclear Burst Wave Problems.
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