2.4  Axisymmetric Surfaces


In the subroutines that solve axisymmetric acoustic problems ( AIBEMA, AEBEMA and AMBEMA) the boundaries must be represented in the form of a set of truncated cone shells. In axisymmetric problems the surface can be defined by specifying the points on the generator and sweeping through 2p. In order that the normal to the boundary points outward rather than inward the two nodes that define each element must be listed in the clockwise direction around the generator of the boundary. The programs AIBEMA_T, AEBEMA_T and AMBEMA_T each solve acoustic problems in which the boundary under consideration is that of a sphere of unit radius. The boundary is represented by 18 truncated cone shells and has 19 vertices and it is illustrated in Figure 2.5.
Fig 2.5. Representation of the sphere by truncated cone shells.

In order to pass the description of the boundary to the subroutines it is represented by the two tables of data 2.E and 2.F. Table 2.E lists the (r,z) coordinates of the vertices and is identified by the real array VERTEX. Table 2.F lists the index of the two vertices that define each panel and is identified by the integer array SELV.

Table 2.E: Vertices of sphere generator ( VERTEX)
Index r z Index r z
1 0.000 1.000 11 0.985 -0.174
2 0.174 0.985 12 0.940 -0.342
3 0.342 0.940 13 0.866 -0.500
4 0.500 0.866 14 0.766 -0.643
5 0.643 0.766 15 0.643 -0.766
6 0.766 0.643 16 0.500 -0.866
7 0.866 0.500 17 0.342 -0.940
8 0.940 0.342 18 0.174 -0.985
9 0.985 0.174 19 0.000 -1.000
10 1.000 0.000

Table 2.F: Panels that constitute the sphere ( SELV))
Index Vertex 1 Vertex 2 Index Vertex 1 Vertex 2
1 1 2 10 10 11
2 2 3 11 11 12
3 3 4 12 12 13
4 4 5 13 13 14
5 5 6 14 14 15
6 6 7 15 15 16
7 7 8 16 16 17
8 8 9 17 17 18
9 9 10 18 18 19

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