7 Concluding Discussion
The computational solution of a given acoustic radiation problem
first involves the selection of an appropriate acoustic radiation
model which underlies the choice of method. For example the model
of a closed surface in an infinite acoustic medium underlies the
boundary element method (see, for example, Schenck [2] or
Kirkup and Henwood [5]). Several practical acoustic problems
are suitably represented by the acoustic radiation model of
figure 1 and thus a computational solution can be obtained via methods based on
the Rayleigh integral. For example the Rayleigh integral model
can be applied to the problem of predicting the noise radiated by the
faces of an in-line engine block (see Yorke [11]
or Kirkup and Tyrrell [12],
for example).
Computational methods based on the Rayleigh integral have been applied to certain
classes of acoustic problems for some time. However, such methods have
generally been based on direct numerical integration and hence they
have poor numerical properties. In this paper product integration
has been applied to the Rayleigh integral to derive a more robust method,
that is more in line boundary element methodology.
A particular implementation of the RIM is described in this paper. In
figure 5 computed and exact sound pressures along the axis of the
circular piston are compared. The results appear to be in good
agreement. In figure 7 the computed radiation ratio curves for the
first sixteen modes of a hinged square panel are given. These
compare well with similar results given in Wallace [13].
The Rayleigh integral method is applicable to acoustic problems that
include of a flat or nearly flat panel exposed to an acoustic medium
on one side. Since the method requires the description of the
panel as a set of elements (triangles) then the panel may be of
arbitrary shape. Hence the Rayleigh integral method should
serve as a useful addition to acoustic software libraries.
Acknowledgement. The author is grateful to Mr. R. J. Tyrrell of
International Automotive Design, Worthing and to Dr. D. J. Henwood
of the Department of Mathematical Sciences, Brighton Polytechnic for
their advice on the work in this paper.