Matching of fundamental modes at a junction of a cylinder and a truncated cone; application to the calculation of some radiation impedances
Abstract
The problem of the junction between a cylinder and a truncated cone at
frequencies below the first cutoff of the cylinder is investigated, in
particular for the case of acute angles. An analytical model of the matching
of a cylinder and a truncated cone is derived for the general case of a cone
of finite length having a known terminal impedance. When the cone is
infinite and the angle is right, the problem is similar to the classical
problem of a tube radiating in an infinite baffle. The model is based on a
general formulation of the junction of several waveguides at low frequencies
(when only the fundamental mode propagates in each guide), and on the
assumption that at high frequencies, the radiation impedance of the cylinder
is equal to its characteristic impedance. The model has the form of an
equivalent circuit, and involves several parameters related to the geometry
(the areas of the surfaces defining the matching cavity and the volume of
this cavity). In addition, the model requires one supplementary parameter
only, i.e., the zero frequency value of the added mass (or length
correction), which has to be determined numerically (the Finite Element
Method is used). Analytical and numerical results agree very well at low and
moderate frequencies, up to the cutoff of the first higher-order mode. For
the radiation into an infinite flange, the results improve upon those in a
recent publication that were obtained by optimization. The case of obtuse
angles is more complicated and is briefly discussed. Finally for the case of
infinite cones, the reflection coefficient is compared to that obtained in
previous studies.
Origin : Files produced by the author(s)
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