The test problem is that of a uniformly vibrating circular piston of radius 0.1,
centred at (0,0,0)
at wavenumbers k=10 and k=25. If v(p) = -V (p Î G) is the velocity of the
piston (uniform over its surface) then the sound pressure P(p)
at a point p=(p1, p2, p3) on the axis of the piston is given by
P(p) = rc V ( ei k (0.01 + p32 )[1/2] - ei k p3 )
see, for example, Skudrzyk [10], pp631-633.
The circular piston is divided into 24 triangles, as shown in figure 4.
Figures 5 compare the computed and exact on axis sound pressure obtained from the
subroutine at twenty points with exact values.
The second test problem is that of a uniform square panel with its sides
hinged onto an infinite rigid baffle. The [0,1] ×[0,1] square is
vibrating in its natural modes which are
v(p) = sin(l pp1) sin( m pp2) (p Î G)
(17)
where l and m are integers. The property that is of interest is the
radiation ratio of the panel vibrating in each of its mode shapes (17).
In order to apply the subroutine to the problem, the square panel is divided into
64 triangles, as shown in figure 6. The mode shapes considered were the sixteen
given by putting l=1,2,3,4 and m=1,2,3,4 in (17). The wavenumbers
at which the radiation ratio is computed are k = 0.0, 0.2, 0.4, ..., 34.8, 35.0 .
Figures 7 show the radiation ratio curves constructed from the results of the
subroutine run.
