A Diffraction Problem and Crack Propagation

1967 ◽  
Vol 34 (1) ◽  
pp. 100-103 ◽  
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.

Stresses Produced in a Half Plane by Moving Loads

1958 ◽  
Vol 25 (4) ◽  
pp. 433-436
Author(s):  
J. Cole ◽  
J. Huth
Keyword(s):  
Stress Field ◽  
Elastic Medium ◽  
Half Plane ◽  
Load Distribution ◽  
Wave Speed ◽  
Complete Solution ◽  
Moving Loads ◽  
Concentrated Load ◽  
Line Load ◽  
Wave Speeds

Abstract A study is made of stresses and displacements induced in an elastic half plane (plane strain) by a concentrated line load moving at a constant speed along its surface. The stress field for an arbitrary load distribution can be built up by superposition of these concentrated-load solutions. Three cases are considered: (a) The load is moving more slowly than either the longitudinal or transversal wave speeds of the elastic medium (subsonic case). (b) The load speed is between the two wave speeds (transonic case). (c) The load speed is greater than either wave speed (supersonic case). In each of these cases the nature of the singularity caused by the load is examined and the complete solution is given.

Leaky and surface wave diffraction by an asymmetric impedance half plane

1983 ◽  
Vol 61 (6) ◽  
pp. 906-918
Author(s):  
W. Nasalski
Keyword(s):  
Exact Solution ◽  
Surface Wave ◽  
Half Plane ◽  
Wave Diffraction ◽  
Isotropic Medium ◽  
Diffraction Problem ◽  
Optical Field ◽  
Point Of View ◽  
Leaky Wave ◽  
Uniqueness Of The Solution

An exact solution is obtained for the problem of a leaky or surface wave incident on an impedance half plane in a homogeneous, isotropic medium. The impedance half plane is asymmetric, i.e., with different constant surface impedances at the upper and lower faces, respectively. The incident leaky wave propagates in a direction normal to the edge of the half plane.The diffraction problem leads to a set of two coupled Wiener–Hopf equations, from which two Hilbert problems on a new contour are obtained and solved. The Wiener–Hopf–Hilbert method is used. Expressions for the geometrical optical field are also derived and results arc discussed from the point of view of the uniqueness of the solution.

Transverse surface waves in magneto-elasticity

1966 ◽  
Vol 62 (3) ◽  
pp. 541-545 ◽  
Author(s):  
C. M. Purushothama
Keyword(s):  
Magnetic Field ◽  
Wave Propagation ◽  
Surface Waves ◽  
Elastic Medium ◽  
Uniform Magnetic Field ◽  
Shear Waves ◽  
Plane Shear ◽  
Electrically Conducting ◽  
Velocity Of Propagation

AbstractIt has been shown that uncoupled surface waves of SH type can be propagated without any dispersion in an electrically conducting semi-infinite elastic medium provided a uniform magnetic field acts non-aligned to the direction of wave propagation. In general, the velocity of propagation will be slightly greater than that of plane shear waves in the medium.

Diffraction of a pulse by a resistive half-plane. I. Normal incidence

1960 ◽  
Vol 255 (1283) ◽  
pp. 538-549 ◽  
Keyword(s):  
Time Dependence ◽  
Half Plane ◽  
Wave Diffraction ◽  
Diffraction Problem ◽  
Normal Incidence ◽  
Step Function ◽  
Two Dimensional ◽  
Dynamic Similarity ◽  
Function Time ◽  
Dimensional Wave

The two-dimensional wave diffraction problem, acoustic or electromagnetic, in which a pulse of step-function time dependence is diffracted by a resistive half-plane is solved by assuming dynamic similarity in the solution.

Diffraction by a half plane perpendicular to the distinguished axis of a gyrotropic medium (oblique incidence)

1981 ◽  
Vol 59 (3) ◽  
pp. 403-424 ◽  
Author(s):  
S. Przeździecki ◽  
R. A. Hurd
Keyword(s):  
Half Plane ◽  
Fourier Transforms ◽  
Boundary Value ◽  
Diffraction Problem ◽  
Closed Form Solution ◽  
Second Order ◽  
Dimensional Case ◽  
Two Dimensional ◽  
Dimensional Solution ◽  
Electromagnetic Plane Wave

An exact, closed form solution is found for the following half plane diffraction problem. (I) The medium surrounding the half plane is gyrotropic. (II) The scattering half plane is perfectly conducting and oriented perpendicular to the distinguished axis of the medium. (III) The direction of propagation of the incident electromagnetic plane wave is arbitrary (skew) with respect to the edge of the half plane. The result presented is a generalization of a solution for the same problem with incidence normal to the edge of the half plane (two-dimensional case).The fundamental, distinctive feature of the problem is that it constitutes a boundary value problem for a system of two coupled second order partial differential equations. All previously solved electromagnetic diffraction problems reduced to boundary value problems for either one or two uncoupled second order equations. (Exception: the two-dimensional case of the present problem.) The problem is formulated in terms of the (generalized) scalar Hertz potentials and leads to a set of two coupled Wiener–Hopf equations. This set, previously thought insoluble by quadratures, yields to the Wiener–Hopf–Hilbert method.The three-dimensional solution is synthesized from appropriate solutions to two-dimensional problems. Peculiar waves of ghost potentials, which correspond to zero electromagnetic fields play an essential role in this synthesis. The problem is two-moded: that is, superpositions of both ordinary and extraordinary waves are necessary for the spectral representation of the solution. An important simplifying feature of the problem is that the coupling of the modes is purely due to edge diffraction, there being no reflection coupling. The solution is simple in that the Fourier transforms of the potentials are just algebraic functions. Basic properties of the solution are briefly discussed.

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