The aim of the work reported in this thesis is to establish a generic approach for the
study of the propagation of higher-order modes in ducts of circular cross section when a
simple aperture device is installed in the duct. Additionally to describe the effects of the
simple aperture device on the whole in duct acoustic field, especially in the frequency
range after the first higher-order mode cuts on. The approach, which is based on
approximating each higher-order mode as an uncoupled mode, requires an accurate and
effective decomposition of the in duct field in the higher frequency range.
In the theoretical work for the propagation of the higher-order modes in circular ducts,
one established model to describe the open end of the duct is considered. Another model
to describe the sound source (both plane wave source and point source) and the
boundaries between the aperture device and the main duct is proposed. Combining the
two models together, a revised model to describe the whole acoustic system is obtained
and used to carry out the in duct field decomposition in the higher frequency range.
From this the amplitudes of various higher-order modes are obtained. Experimental
investigations have also been carried out to determine the applicability of this model.
The experimental work can be divided into two groups: reference measurements for the
inputs to the models and direct measurements of the sound fields. The reference
measurements are used to obtain the strength of the sound source. The direct
measurements are used to compare with the results obtained from the theoretical
calculations. Through the comparison, the errors and the applicability of the theoretical
model are established. It is shown that this approach to the problem may be used in the
normalized wave number region up to k * R -< 7 , which is nearly four times the plane
wave region and includes sixteen propagating higher-order modes.
By determining the amplitudes of the higher-order modes, the whole in-duct acoustic
field is fully decomposed into individual model contributions and can be reconstructed
in detail. In order to get a complete and coordinate-independent description of the effects
of installing different simple aperture devices, the power radiated out of the open end of
- i -
the duct is calculated in the fonn of different single modes. Additionally the insertion
losses for different aperture device situations are also obtained. Then through the
comparison of the powers and the insertion losses, it is possible to find an effective and
direct way to express the effects of installing different simple aperture devices in a duct.
A Doctoral Thesis. Submitted in partial fulfillment of the requirements for the award of Doctor of Philosophy of Loughborough University