A New Approach to Accelerate Frequency-Domain Studies of Complex Structures

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Principal Investigator's Name: J. Gregory McDanielInstitution: Boston UniversityProposal Number: 9978747Proposal Title: A New Approach to Accelerate Frequency-Domain Studies of Complex StructuresProject AbstractCurrently, 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 proposed 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. Preliminary estimates indicate that, for structures of current interest to industry, the reductions in computational times will be several orders of magnitude. The approach is based on the premise that one is typically interested in a structure's dynamic response inside a frequency band. By approximating the effects of modes that resonate outside the band, the matrix equation of motion is reduced in rank. In the proposed approach, this reduction will be achieved by an innovative transformation that uses the forced responses of the structure evaluated at a few sampled frequencies in the band. As the forced responses in the band are mostlycomprised of the modes that resonate in the band, this transformation naturally retains modes lying in the band. The method will be developed in the context of a carefully selected testbed of industry-relevant structural models, ranging from one thousand to one million degrees-of-freedom. The research will be used to enhance undergraduate and graduate education in structural vibrations through the creation of a unique interactive software package entitled the Virtual Vibrations Laboratory, which will allow students to explore fundamental vibration phenomena and vibration control techniques for models of real industry-relevant structures. The explorations will introduce students to topics such as active vibration control, mode localization, and advanced damping treatments. It is expected that this software package will create a new avenue for the involvement of industry in engineering education.