AE02.pdf

The out of plane displacement u 3 peaks about 01 ?

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The out-of-plane displacement u 3 peaks about 0.1 λ below the surface and the surface displacements decrease to negligible levels for depths greater than two wavelengths. Surface waves may exist on free surfaces as well as on surfaces rigidly constrained in both the tangential and the normal directions. Surfaces that have mixed boundary conditions (such as those rigidly constrained from normal motion but with zero in-plane tractions) cannot support surface waves. c v v r = + + 0 87 1 12 1 . . α α κ α κ 6 + ( ) + ( ) = 8 24 16 16 1 0 4 2 2 2 u jk e a e e j t kx qx sx 3 = × × ( ) ω 1 3 3 1 1 2 2 u 2 0 = u k e a a e a e j t kx qx sx 1 2 2 2 2 1 3 3 1 1 2 1 1 = × × ( ) ω κ u A e j k x t 1 1 1 = × ( ) real part of ω u A e j k x t 1 1 1 = ( ) ( ) ω T f = 1 f c λ = 1 82 Acoustic Emission Testing
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The fact that the wave in Eqs. 62 to 64 is propagating in the x 1 direction is entirely arbitrary. A similar solution exists for a surface wave traveling in any direction parallel to the surface. Although surface waves and bulk waves are independent of each other in a semiinfinite solid with a free surface, they do couple in solids that have intersecting surfaces (corners) or surfaces with boundary conditions that change with position on the surface. Coupling between surface waves and bulk waves is difficult to avoid in solids of practical geometries. Reflection of Waves at Interfaces Waves that encounter a change in the media in which they are propagating will change directions or reflect. In addition to reflection, the interface causes the wave to diverge from its original line of flight or refract in the second medium. Also, the mode of the wave may be changed in the reflection process. A wave incident upon an interface between two media will reflect or refract such that the directions of the incident, reflected and refracted waves all lie in the same plane. This plane is defined by the line along which the incident wave is propagating and the normal to the interface. Transverse Waves Incident on Free Surface For a transverse wave incident on a free surface, it is convenient to decompose the wave into a component normal to the plane of reflection ( SH ) and a component that lies in the plane of reflection ( SV ). The reflection of the SH component is the simplest case because only an SH wave is reflected at an angle equal to the incident angle. The reflected SH wave is equal in magnitude (but of opposite sign) to the amplitude of the incident SH wave. Thus, an SH wave reflects in the same way that a beam of light reflects from a mirror, with only a change in the direction of the wave’s travel. The reflection of an SV wave is more complicated.
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  • Fall '19
  • Nondestructive testing, Acoustic Emission, Acoustic Emission Testing

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