8 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, Kirkup [5]).
Several practical acoustic problems
are suitably represented by the acoustic radiation model of
a vibrating plate lying in an infinite baffle
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 [15]
or Kirkup and Tyrrell [2], Seybert et al [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
figures 3 and 4, computed and exact sound pressures along the axis of the
circular piston are compared. The results appear to be in good
agreement. In figure 6 and 7 the computed radiation ratio curves for the
a square plate in a simple motion are given. These may be
compared with similar results given in Wallace [14].
The Rayleigh integral method is applicable to acoustic problems that
include of a flat or nearly flat plate exposed to an acoustic medium
on one side. Since the method requires the description of the
plate as a set of elements (triangles) then the plate may be of
arbitrary shape. Hence the Rayleigh integral method should
serve as a useful addition to acoustic software libraries.