11Focusing of Multiple Acoustic Edge Waves Diffracted at a Convex Body of Revolution with a Flat Base
The theory presented below is based on papers by Ufimtsev (1989, 1991).
11.1 Statement of the Problem and its Characteristic Features
This problem is illustrated in Figure 11.1, which shows a convex body of revolution excited by the axisymmetrical incident wave constant along the edge.
The axis of symmetry (z-axis) is a focal line for elementary edge waves and rays. With respect to the observation points P on this axis, each diffraction point at the edge is a point of the stationary phase. The elementary rays propagate in the directions of the edge-diffraction cones, which transform (in this particular case) into the meridian planes. Because of that, the directivity pattern of elementary edge rays are expressed in terms of the Sommerfeld functions f and g, as shown in Sections 7.6 and 8.1. The functions f and g are defined in Equations (2.62) and (2.264), and they describe the field generated by the total scattering sources jtots, h = js, h(0) + j(1)s, h induced near the edge. Analysis of this field is the main objective of this chapter.
Figure 11.1 Body of revolution excited by the source Q. Focusing of diffracted edge waves occurs at points P on the z-axis. [Reprinted ...
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