Reflection, radiation, and coupling of higher-order modes at discontinuities in finite-length rigid-walled rectangular ducts

Abstract

The effects of discontinuities on higher order modes is important in the design of passive and active noise control systems in ducts which operate near or above the cutoff frequency of the duct. Accurate acoustic monitoring of mechanical systems in ducts at frequencies near and above the cutoff frequency of the first mode must include the effects of discontinuities. This thesis examines the reflection, transmission, and coupling of higher order modes at discontinuities in finite length rigid walled rectangular ducts. Using a method of generalized scattering coefficients, analytic expressions for the reflection and transmission of higher order modes at size discontinuities, junctions, and baffled terminations are developed. A technique to measure the higher order modes is discussed and implemented. When written in matrix form, the equations for the reflection and transmission coefficients for all three discontinuities take on the standard form for reflection and transmission of plane waves at a change of impedance. For all the examples given, the magnitude of the mutual coupling coefficients can be significant, often larger than that of the self reflection and transmission coefficients, showing that modal coupling must be included when working with models near and above the cutoff frequency of the first higher order mode. Analytic expressions for the reflection and transmission coefficients of a general multi-port junction are derived in terms of the Green's function of the junction region. Examples of a right angle bend and a T junction are given. It is shown that the magnitude xx Big thanks go to the greatest set of administrative assistants at Penn State, Karen Brooks, Catherine Brown, Barbara Crocken, and Carolyn Smith for all their help throughout the years.

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