Statistical Elastodynamics of Large Structures

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PI Name: Richard L. WeaverInstitution: University of Illinois at Urbana-ChampaignProposal Number: 0201346Proposal Title: Statistical Elastodynamics of Large StructuresProject Abstract This project investigates the statistics of vibrational and acoustic energy, its mean flow and its fluctuations, in complex irregular reverberant structures. The work is conceived with a view towards improved statistical energy theories for the mid-frequency range in such structures, and involves numerical simulations, analytic theory and laboratory measurements.The project consists of two complementary thrusts. A method for efficient estimation of flow of mean energy will be extended to the time dependent case, and tested by comparing with results from direct numerical simulation and conventional Statistical Energy Analysis. Comparisons will be carried out on models and structures from industrial applications. The l variance of fluctuations away from that mean will be investigated using Random Matrix Theory and compared with laboratory measurements and numerical simulations.Technical impact will be in the creation of better statistical energy models for the vibrations and acoustics of large structures, with implications for noise and vibration design for consumer machinery, and space and naval structures. Other applications will lie in reverberation room acoustics, ultrasonics, stochastic seismic waves, mesoscopic electronics, and diffuse optics for lidar and medical imaging. Broader impact is ensured by the industrial collaborations that are envisioned, by collaborations with seismologists and physicists, by archival publications, by the training of PhD students, by the PI's participation in technical meetings, and by his introduction of new material in advanced courses, with new software on statistical energy analysis.