CAREER: Accelerated Analyses of Complex Structures by Frequency-Windowed Condensations

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Proposal Title: "CAREER: Accelerated Analyses of Complex Structures by Frequency-Windowed Condensations" Proposal Number: 9984994AbstractThis CAREER project involves integrated research and educational activities whose focus is a new approach to analyzing the vibrations of complex vibrating structures. Currently, efforts to model the vibrations of complex structures are severely limited by the computational expenses incurred in finding either the modal properties or the forced responses of the structures. The research could dramatically reduce these expenses, and hence enable more complete and accurate vibration studies, by developing a novel means of condensing the dynamic equations of motion. This condensation will be achieved by an innovative transformation that uses the forced responses of the structure evaluated at a few sampled frequencies in the band. Preliminary estimates indicate that, for structures of current interest to industry, the reductions in computational times will be several orders of magnitude. Two industrial collaborators will provide finite element models of complex structures for use in developing and demonstrating the proposed approach. Educational activities include the development, use, and assessment of a unique computer-based educational resource that allows students to interactively explore the vibrations of real-world structures. When combined with a course module that introduces students to the vibrations of many degree-of-freedom systems, the resource is expected to complement studies of lumped-parameter models that are currently the focus of undergraduate vibration curriculums. By employing the research method to expedite response calculations, the package will allow students to interactively explore vibration phenomena for industry-supplied models of real structures. It is expected that this package will create a new avenue for the involvement of industry in engineering education.