This project continues work initiated in an earlier effort dealing with the phenomenon of vibration isolation in structures with parametric uncertainties and irregularities, and focusing on generating fundamental insights into the physical mechanisms of localization from the study of generic idealized models of periodic structures. The current project looks at three issues which are (a) the evaluation and prediction of the significance of localization effects in engineering structures, (b) the development of concise statistical tools for the analyst and designer confronted with uncertainties in structural dynamics applications, and (3) the use of these novel techniques and insights to develop a theory for vibration transmission in complex structures. An experimental verification of localization effects will be performed on a multi-span beam. The impact of the work is clear. Many large structures, i.e., truss beams, turbomachinery rotors, submarine hulls, overhead power lines, etc., are periodic. Their design and analysis is based on the assumption that the periodicity is perfect. This not the case, and often periodic structures can be highly sensitive to small irregularities in manufacturing tolerances. Neglecting these variations may lead to erroneous results and serious consequences. This research focuses on correcting this problem through development of new techniques for vibrational analysis of large periodic structures.
