Mid-Frequency Vibration Analysis of Complex Structures

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The main emphasis of this research project is to develop methods for analyzing and predicting mid-frequency vibration transmission in complex structures, which are assemblages of connected substructures. Complex structures are a generalization of periodic and nearly periodic structures. In the mid-frequency range of vibration for a complex structure, the vibration wavelengths are small enough for uncertainties and flaws in the structure to have significant impact on the global dynamics. The assumptions which currently limit high-frequency statistical energy methods are systematically examined and relaxed. This extends their applicability to more general systems such as those with strong inter-component coupling. A major thrust in this research effort is on the elimination of assumptions which restrict the analysis to the high-frequency range. The outcome of this research is a hierarchy of new methods for the vibration analysis of complex structures. These new methods are valid for both mid-and high-frequency ranges, reproduce mode localization and related phenomena caused by uncertainties, which handle moderate and strong coupling situations, and are relatively simple. The methods developed are validated through systematic comparison with experimental data. Simple benchmark experiments (e.g., vibration transmission in two coupled plates) are carried out in the laboratory.