An exact solution for diffraction of a line-source field by a half-plane

Much of the work on the theory of diffraction by an infinite wedge has been for cases of harmonic time-dependence. Oberhettinger (1) obtained an expression for the Green's function of the wave equation in the two dimensional case of a line source of oscillating current parallel to the edge of a wedge with perfectly conducting walls. Solutions of the time-dependent wave equation have been obtained by Keller and Blank (2), Kay (3) and more recently by Turner (4) who considered the diffraction of a cylindrical pulse by a half plane.

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Diffraction of impulsive elastic waves by a fluid cylinder

Mathematical Proceedings of the Cambridge Philosophical Society ◽

10.1017/s0305004100048611 ◽

1974 ◽

Vol 75 (3) ◽

pp. 391-404 ◽

Cited By ~ 2

Author(s):

Ramanand Jha

Keyword(s):

Exact Solution ◽

Circular Cylinder ◽

Elastic Medium ◽

Elastic Waves ◽

Line Source ◽

Inviscid Fluid ◽

Geometrical Theory ◽

Shadow Zone ◽

Integral Transformations ◽

Geometrical Theory Of Diffraction

AbstractIn this paper, the problem of diffraction of an impulsive P wave by a fluid circular cylinder has been considered. The cylinder is embedded in an unbounded isotropic homogeneous elastic medium and it is filled with inviscid fluid material. The line source, giving rise to the incident front, is situated outside the cylinder parallel to its axis.The exact solution of the problem is obtained by using the method of dual integral transformations. The solution is evaluated approximately to obtain the motion on the wave front in the shadow zone of the elastic medium. Further, we interpret the approxi mate solutions in terms of Keller's geometrical theory of diffraction. Our result also gives a correction to an earlier investigation of the similar problem by Knopoff and Gilbert(s).

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Vertex generated waves outside metallic wedges

Mathematical Proceedings of the Cambridge Philosophical Society ◽

10.1017/s0305004100035349 ◽

1961 ◽

Vol 57 (2) ◽

pp. 393-400 ◽

Cited By ~ 4

Author(s):

W. E. Williams ◽

L. Rosenhead

Keyword(s):

Exact Solution ◽

Difference Equation ◽

Boundary Value Problem ◽

Surface Impedance ◽

Line Source ◽

Complete Agreement ◽

Magnetic Line ◽

Arbitrary Angle ◽

Surface Reactance ◽

The Waves

ABSTRACTA study is made of the waves generated by a magnetic line source placed at the vertex of a wedge of high conductivity and arbitrary angle. The boundary-value problem is reduced to the solution of a difference equation and an exact solution obtained. The method is also applied to the case of dielectric coated wedges where the surface reactance and resistance are arbitrary, and the propagation of surface waves along such surfaces is considered briefly. The forms of the solution for large and small values of the surface impedance are obtained and show complete agreement with the known results available for a right-angled wedge and a plane.

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Exact solution of the problem of stretching a half-plane with a crack reaching the boundary

Soviet Applied Mechanics ◽

10.1007/bf00883172 ◽

1975 ◽

Vol 11 (2) ◽

pp. 221-222

Author(s):

Yu. Z. Povstenko

Keyword(s):

Exact Solution ◽

Half Plane

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A Diffraction Problem and Crack Propagation

Journal of Applied Mechanics ◽

10.1115/1.3607607 ◽

1967 ◽

Vol 34 (1) ◽

pp. 100-103 ◽

Cited By ~ 9

Author(s):

A. Jahanshahi

Keyword(s):

Exact Solution ◽

Stress Field ◽

Crack Propagation ◽

Elastic Medium ◽

Half Plane ◽

Diffraction Problem ◽

Shear Waves ◽

Stress Waves ◽

Plane Crack ◽

Antiplane Strain

The exact solution to the problem of diffraction of plane harmonic polarized shear waves by a half-plane crack extending under antiplane strain is constructed. The solution is employed to study the nature of the stress field associated with an extending crack in an elastic medium excited by stress waves.

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