CiteULike: norris rigid

The Born approximation in the theory of the scattering of elastic waves by flaws

JE Gubernatis — 2007-03-27T17:16:52-00:00

Journal of Applied Physics, Vol. 48, No. 7. (1977), pp. 2812-2819.

We used the integral equation formulation of the scattering of elastic waves to generate an approximate solution analogous to the Born approximation in quantum mechanics. This solution is attractive because of the ease with which it may be applied to scatterers of complicated shapes. We investigated the validity of the approximation by comparing it with exact results for spherical scatterers. Our conclusion for voids in elastic media is that the approximation describes well the scattering when the wavelength of the incident wave is approximately an order of magnitude larger than the scatterer and when the scattering is viewed in the backscattered directions. For many applications this range of validity is experimentally accessible. For elastic inclusions, however, where the properties of defect and host differed by 20–40%, the Born approximation is surprisingly good for all angles and even at short wavelengths. Journal of Applied Physics is copyrighted by The American Institute of Physics. doi:10.1063/1.324142 PACS: 62.30.+d, 03.40.Kf, 81.70.+r, 91.30.-f Additional Information Full Text: [ PDF (889 kB)

Scattering of a Plane Transverse Wave by a Spherical Obstacle in an Elastic Medium

Norman Einspruch — 2007-03-27T17:12:58-00:00

Journal of Applied Physics, Vol. 31, No. 5. (1960), pp. 806-818.

An analysis of the scattering of transverse elastic waves by spherical obstacles is presented. The scatterer is taken to be (a) a cavity, (b) a rigid sphere, (c) a fluid-filled cavity, and (d) to consist of an elastic material with properties different from those of the surrounding material. The problems are carried as far as possible analytically without approximations and are reported as matrix equations. The solution of these equations yields the expansion coefficients that describe the waves which are scattered outward from the obstacle and which are excited within the scatterer. A general expression for the scattering cross section offered to a transverse wave has been derived. The Rayleigh approximation is then considered in detail for three of the cases. ©1960 The American Institute of Physics

Scattering of a Plane Longitudinal Wave by a Spherical Obstacle in an Isotropically Elastic Solid

CF Ying — 2007-03-27T17:10:55-00:00

Journal of Applied Physics, Vol. 27, No. 9. (1956), pp. 1086-1097.

Scattering by a spherical obstacle of a plane longitudinal wave propagating in an isotropically elastic solid is computed. Expressions for the scattered wave and the total scattered energy are given. Three special types of obstacle—an isotropically elastic sphere, a spherical cavity, and a rigid sphere—are discussed in detail, especially for Rayleigh scattering. The result for the isotropically elastic sphere is compared with the well-known result of scattering of a plane wave propagating in an ideal fluid by a sphere of another ideal fluid. Journal of Applied Physics is copyrighted by The American Institute of Physics.

Response of a Rigid Spheroidal Inclusion to an Incident Plane Compressional Elastic Wave

SK Datta — 2007-03-26T16:59:08-00:00

SIAM Journal on Applied Mathematics, Vol. 26, No. 2. (1974), pp. 350-369.

Dyadic Scattering by Small Obstacles. The Rigid Sphere

George Dassios — 2007-03-26T13:51:22-00:00

Q J Mechanics Appl Math, Vol. 54, No. 3. (1 September 2001), pp. 341-374.

The general theory of low-frequency dyadic scattering is developed for the near fields, the far fields and all the energy functionals associated with scattering problems. The incident field could be any complete dyadic field generated either in the exterior medium of propagation (point source) or at infinity (plane waves). The case of a small rigid sphere, which is illuminated by a plane dyadic field, is solved and the corresponding results for acoustic and elastic scattering are recovered as special cases. In order to solve analytically the sphere problem a special technique had to be developed, which generates Papkovich-type differential representations of dyadic elastostatic displacements. Comparison of numerical results, obtained via the boundary element method, show an amazing accuracy with our analytical results. 10.1093/qjmam/54.3.341

Scattering of Sound by a Rigid Movable Sphere

Robert Hickling — 2007-03-26T13:15:10-00:00

The Journal of the Acoustical Society of America, Vol. 39, No. 2. (1966), pp. 276-279.

The echoes from a rigid, freely movable sphere, due to an incident train of plane waves, are computed, together with the associated rigid-body motions of the sphere. These results are compared with those for a rigid, immovable sphere and it is shown that they differ significantly only for values of ka below about 5. The significance of the results in relation to previous work on sonar echoes from solid, elastic spheres in water is discussed. A particular case of forced motion of the rigid sphere, where the echoes diminish to zero at high frequencies, is also investigated. ©1966 Acoustical Society of America

The disturbance of a plane dyadic wave by a small spherical cavity

George Dassios — 2007-03-26T13:07:17-00:00

International Journal of Engineering Science, Vol. 40, No. 17. (October 2002), pp. 1975-2000.

Scattering of a Spherical Dyadic Field by a Small Rigid Sphere

George Dassios — 2007-03-26T12:59:45-00:00

Mathematics and Mechanics of Solids, Vol. 7, No. 1. (1 February 2002), pp. 3-40.

A complete dyadic field, which is generated at a point and propagates within a homogeneous and isotropic elastic medium, is disturbed by a small rigid sphere. Analytic solutions for this complicated dyadic scattering problem are provided with the help of an extended theory of the Papkovich representation for elastostatic dyadic fields. Relative results obtained numerically show an amazing coincidence as long as we stay in the low-frequency regime. In contrast to the plane wave excitation case, where only a few multipole terms are needed to express the leading low-frequency approximations, the case of point source excitation provides low-frequency solutions where an infinite number of multipoles are present. An exception is offered by the first-order approximation, which enjoys a closed-form expression. 10.1177/1081286502007001219

Scattering of elastic waves by a movable rigid sphere embedded in an infinite elastic solid

Y Iwashimizu — 2007-03-26T12:53:07-00:00

Journal of Sound and Vibration, Vol. 21, No. 4. (22 April 1972), pp. 463-469.

Scattering of an elastic wave by a rigid but movable spherical obstacle is studied, its oscillation being taken into account. The scattered wave, the oscillation of the rigid sphere and the scattering cross section are calculated for an incident longitudinal or shear wave. These calculations reveal the differences between the scattering by a movable rigid sphere and that by an immovable one, especially in the Rayleigh limit. The scattering cross section in this limit is shown to depend on the inverse of the fourth power of the wavelength, while it was reported to be independent of the wavelength for an immovable rigid sphere.