1 Introduction
The purpose of this work is to develop a method and Fortran
subroutine that delivers a computational solution to the
acoustic field
surrounding a (set of) flat plate(s) with specified acoustic properties, lying
in an infinite baffle. The physical situation is illustrated
in figure 1.
The acoustic domain
is the three-dimensional half-space.
The motion of the plate P is governed
by a given condition on the plate. The baffle is rigid and
perfectly reflecting. This model can be applied to a
range of acoustic problems. For example it can model the
acoustic field around the near-flat surface of an object.
Computational methods for solving this problem are based on the
Rayleigh integral [10] which directly relates the
velocity potential (or sound pressure) in the acoustic domain to
the velocity distribution on the plate.
Methods obtained in this way have been derived and applied
to the problem of computing the properties of the acoustic field
exterior to a flat or near-flat plate for some time.
These methods are generally derived through applying a direct numerical
integration method (see, for example Schenck [11])
to the Rayleigh integral. The resulting method is often termed the
simple source method.
However, the integrand of the Rayleigh integral can be singular
or near-singular and it becomes increasingly oscillatory as the
wavenumber increases. Hence the direct numerical integration
that underlies the simple source method is likely
to be a computationally inefficient means of obtaining the solution
in many cases.
In the author's PhD [2] and in the paper [4]
a method derived through numerical product integration of the Rayleigh
integral (for the Neumann condition on the plate)
was formally introduced and demonstrated.
The method
is termed the Rayleigh integral method and it is superior
to the simple source method since its accuracy is virtually unaffected
by the nature of the integrand.
The Rayleigh Integral Method is extended to cover similar
problems but with a wider range of boundary conditions in this document.
A Fortran subroutine ( RIM3) that implements the method
for three-dimensional acoustic problems is developed.
Test problems have been written to demonstrate the
method. The results from a range of test problems are given.
The subroutine RIM3, the test problems and the
other necessary software is provided with this article.