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.

Mufflers and silencers are commonly used to attenuate noise sources such as internal combustion engines and HVAC systems. Typically, these environments contain mean flow that can affect the acoustic properties of the muffler components and may produce flow generated noise. To characterize the muffler performance, common metrics such as insertion and transmission loss and noise reduction are used in industry. Though transmission loss without flow is often measured and is a relatively simple bench top experiment and useful for model validation purposes, mean flow can significantly affect the muffler performance. There are a few existing and commercial transmission loss rigs that incorporate flow into the measurement procedure. These rigs are useful for model verification including flow but do not predict how the muffler will perform in the system since the source, termination, and pipe lengths significantly impact performance. In this research, the development of an insertion loss test rig is detailed. This testing strategy has the advantage of being simpler, quantifying the self-generated noise due to flow, and taking into account the effect of tailpipe length and a realistic termination. However, the test does not include the actual source and is not as useful for model validation. An electric blower produces the flow and a silencer quiets the flow. Loudspeakers are positioned just downstream of the flow silencer and they are used as the sound source. The low frequency source is a subwoofer installed in a cylindrical enclosure that includes a conical transition from speaker to pipe. Special care is taken to reduce any flow generated noise. Qualification of the system is detailed by comparing the measured transmission loss, noise reduction, and insertion loss to one-dimensional plane wave models. The results demonstrate that the developed rig should be useful as a muffler evaluation tool after a prototype has been constructed. The rig can also be used for transmission loss and noise reduction determination which will prove beneficial for laboratory testing.