Statistical energy methods for vibration transmission analysis of complex structures.

Vibration transmission analysis is important to understand vibration problems occurring in dynamic structures. Dynamic structures consist of several substructures which exchange vibration power through couplings. This vibration power flows from high to low vibration power substructures, and causes vibration problems, deteriorating safety and quality. Thus, in order to understand vibration problems, the flow of vibration power must be identified. This flow can be examined by vibration transmission analysis. Over the past 30 years, the Statistical Energy Analysis (SEA) has been developed for vibration transmission analysis since Lyon established. SEA is an efficient method to statistically analyze vibration transmission in structures of similar design construction, but its application is limited to high frequency ranges, in which SEA ignores the difference between probability density functions (pdfs) of individual modal parameters because modal responses are assumed to be strongly overlapped. In mid-frequency ranges, pdfs of individual modal parameters must be considered for accurate analysis because modal responses are no longer strongly overlapped. Therefore, the main goal of this dissertation is to propose accurate methods for mid-frequency vibration transmission analysis, while maintaining the efficiency of SEA. This dissertation investigates SEA, and proposes a Parameter-based Statistical Energy Method (PSEM) which relaxes SEA assumptions related to strong modal overlap. PSEM is proven to be accurate as well as efficient for vibration transmission analysis in a weakly mono-coupled two-bar system. This study also shows that the applicability of PSEM can be extended to complicatedly coupled structures: a strongly mono-coupled two-bar system, a weakly multi-coupled two-bar system, and weakly-coupled multi-junction four-bar systems. An efficient and accurate approximation is proposed for vibration transmission analysis in a nearly periodic structure (a chain of disordered oscillators), based on SEA. This approximation is also utilized for determining localization factors, which are competitive with the localization factors obtained from the traveling wave formulation in efficiency and accuracy. This dissertation concludes that vibration transmission in complex structures is accurately analyzed by relaxing SEA assumptions, while the SEA advantage--efficiency--is maintained.Ph.D.Applied SciencesAutomotive engineeringMechanical engineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/130446/2/9732055.pd