6Axially Symmetric Scattering of Acoustic Waves at Bodies of Revolution
In this chapter we develop the first-order PTD for acoustic waves scattered at bodies of revolution with sharp edges. Axially symmetric scattering is studied. This situation occurs when an incident plane wave propagates in the direction along the symmetry axis of a body of revolution. An edge of a body of revolution is a circle. When its diameter is much greater than a wavelength, the nonuniform scattering sources j(1)s, h induced near the edge are asymptotically identical to those near the edge of a tangential conic surface consisting of two parts (Fig. 6.1). Diffraction at this surface is an appropriate canonical problem that is studied in Section 6.1. Its solution is used in the next sections to determine the field scattered at certain bodies of revolution.
Figure 6.1 Body of revolution (solid lines) with a circular edge and a conic surface (dashed lines) tangential to a body at the edge points.
6.1 Diffraction at a Canonical Conic Surface
The geometry of the problem is illustrated in Figures 6.1 and 6.2. The solid lines in Figure 6.1 show a general view of a body of revolution with a circular edge. The dashed tangent lines belong to the tangential conic surface. The cross-section ...
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