Series impedances, including source and transfer impedances, are commonly used to model a variety of noise sources and noise treatment elements in duct systems. Particle velocity is assumed to be constant on the plane where the series impedances are defined. The research reported herein details investigations into measuring source and transfer impedance. Especially, the measurement and prediction of the transfer impedance of micro-perforated panel (MPP) absorbers is considered. A wave decomposition method for measuring source impedance and source strength was developed that was purely based on acoustic concepts instead of the equivalent circuit analysis. The method developed is a two-load method. However, it is not necessary to know the impedances of either load a priori. The selection of proper loads was investigated via an error analysis, and the results suggested that it was best to choose one resistive and one reactive load. In addition, a novel type of perforated element was investigated. MPP absorbers are metal or plastic panels with sub-millimeter size holes or slits. In the past, Maa's equation has been used to characterize their performance. However, Maa's equation is only valid for circular perforations. In this research, an inverse method using a nonlinear least square data fitting algorithm was developed to estimate effective parameters that could be used in Maa's theory. This inverse approach was also used to aid in understanding the effect of dust and fluid contamination on the performance of MPP absorbers. In addition, an approach to enhance the attenuation of MPP absorbers by partitioning the backing cavity was investigated experimentally and numerically. Results indicated that partitioning improved the attenuating of grazing sound waves. The effect of modifying both the source and transfer impedances on the system response was also studied using the Moebius transformation. It was demonstrated that the Moebius transformation is a mathematical tool that can be employed to aid in determining and understanding the impact of acoustic impedance modifications on a vibro-acoustic system.

It is shown that the relationship between an impedance change and the dynamic response of a linear system is in the form of the Moebius transformation. The Moebius transformation is a conformal complex transformation that maps straight lines and circles in one complex plane into straight lines and circles in another complex plane. The center and radius of the mapped circle can be predicted provided that all the complex coefficients are known. This feature enables rapid determination of the optimal impedance change to achieve desired performance. This dissertation is primarily focused on the application of the Moebius transformation to enhance vibro-acoustic performance of exhaust systems and expedite the assessment due to modifications. It is shown that an optimal acoustic impedance change can be made to improve both structural and acoustic performance, without increasing the overall dimension and mass of the exhaust system. Application examples include mufflers and enclosures. In addition, it is demonstrated that the approach can be used to assess vibration isolators. In many instances, the source properties (source strength and source impedance) will also greatly influence exhaust system performance through sound reflections and resonances. Thus it is of interest to acoustically characterize the sources and assess the sensitivity of performance towards source impedance. In this dissertation, the experimental characterization of source properties is demonstrated for a diesel engine. Moreover, the same approach can be utilized to characterize other sources like refrigeration systems. It is also shown that the range of variation of performance can be effectively determined given the range of source impedance using the Moebius transformation. This optimization approach is first applied on conventional single-inlet single-outlet exhaust systems and is later applied to multi-inlet multi-outlet (MIMO) systems as well, with proper adjustment. The analytic model for MIMO systems is explained in details and validated experimentally. The sensitivity of MIMO system performance due to source properties is also investigated using the Moebius transformation.