THE USE OF SINGULAR INTEGRALS IN WAVE PROPAGATION PROBLITH APPLICATION TO THE POINT SOURCE IN A SEMI-INFINITE ELASTIC MEDIUM

1963 ◽  
Author(s):  
M. Papadopoulos
Keyword(s):  
Wave Propagation ◽  
Point Source ◽  
Elastic Medium ◽  
Singular Integrals

The use of singular integrals in wave propagation problems; with application to the point source in a semi-infinite elastic medium

1963 ◽  
Vol 276 (1365) ◽  
pp. 204-237 ◽  
Keyword(s):  
Free Surface ◽  
Point Source ◽  
Elastic Medium ◽  
Constant Velocity ◽  
Singular Integrals ◽  
Plane Waves ◽  
Elastic Solid ◽  
Fundamental Solutions ◽  
General Point ◽  
Set Up

This is an investigation of the field due to a general point source of energy in an isotropic, elastic solid with a free surface. The paper is divided into three parts. In part I we are concerned with the development of new plane wave representations for the fundamental solutions of elastodynamics. There are two types of situation involved; we have the simpler type involved in the case of a steady point source which moves steadily with any constant velocity in an elastic medium, this type involves superposition of plane waves with respect to a single parameter, and we have the more complicated transient problem in which a point source is set up at a given moment, and thereafter moves at constant velocity, without change of strength. In part II we make use of the new representation for the field of a steadily moving source in the calculation of fields and displacements in the presence of a free surface and in part III we do the same for the transient source. We discuss in some detail the application of the new approach to the case of a vertical load, to a horizontal load, and to a couple of arbitrary orientation, and we give a general discussion of the singularities to be expected for the general point source.

Comments on a paper by Papadopoulos on the use of singular integrals in wave propagation problems

1965 ◽  
Vol 55 (2) ◽  
pp. 303-318
Author(s):  
I. M. Longman
Keyword(s):  
Wave Propagation ◽  
Point Source ◽  
Singular Integral ◽  
Singular Integrals ◽  
Sound Propagation ◽  
Elastic Solid ◽  
Special Cases

Abstract In a recent paper Papadopoulos [1]1 claims to have obtained solutions to the problem of sound propagation from an impulsive point source in a semi-infinite elastic solid which differ in certain respects from solutions previously obtained by Pekeris [2], [3], and by Pekeris and Lifson [4]. The results of Papadopoulos are based on a singular integral source representation developed by him [5]. By tests based on simple special cases we show that, in a number of cases where Papadopoulos claims a result different from that of Pekeris, the results of Papadopoulos are unacceptable whereas the results of Pekeris are acceptable. Reasons for these errors in Papadopoulos's work are suggested. A number of other errors in the paper of Papadopoulos are also noted. 1 Numbers in brackets refer to references at rear.

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.

Wave Propagation and Parametric Instability in Materials Reinforced by Fibers With Periodically Varying Directions

1975 ◽  
Vol 42 (4) ◽  
pp. 825-831 ◽  
Author(s):  
M. Schoenberg ◽  
Y. Weitsman
Keyword(s):  
Composite Material ◽  
Wave Propagation ◽  
Elastic Medium ◽  
Parametric Instability ◽  
Transversely Isotropic ◽  
Harmonic Waves ◽  
Fiber Reinforced ◽  
Frequency Bands ◽  
Structural Periodicity ◽  
Dominant Direction

This paper concerns the propagation of plane harmonic waves in an infinite fiber-reinforced elastic medium. The composite material is represented by an equivalent homogeneous transversely isotropic matter whose preferred directions coincide with the orientations of the fibers. The fibers are assumed to wobble periodically about a dominant direction, all fibers being parallel to each other. This wobbliness endows the material with a structural periodicity which generates dispersion at all frequencies and instability for various frequency bands. The zones of instability are analyzed in some detail.

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