Modal Identification by Decomposition Methods

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This work is in the area of structural vibrations. New methods will be developed for interpreting test data in order to understand structural vibration properties, with potential applications to aerospace, civil, and mechanical systems.The goal of this proposal is to develop decomposition methods for performing experimental modal analysis. The decomposition methods are performed without measured input signals, which broadens their appeal for modal analysis. The work involves the new state-variable modal decomposition (SVMD), the proper orthogonal decomposition (POD) and the smooth orthogonal decomposition (SOD). In the proposed SVMD, a data-based eigenvalue problem is constructed and related to the generalized eigenvalue problem associated with free-vibration solutions of the state-variable formulation of linear multi-degree-of-freedom systems. The eigenvalues lead to estimates of frequencies and modal damping. The eigenvectors lead to estimates of the mode shapes. The interpretation holds for linear systems with multi-modal freeresponses, whether damping is large or small, modal or nonmodal, and without the need of input data. The connection of the decomposition to the state-variable differential equations provides insight into the application under random excitation. This insight carries over to SOD. Also, the POD is developed to accommodate general mass distributions.Decomposition methods are easy, and need no measured inputs, enabling engineers to master the process with very little learning curve, using basic packages of numerical software, such as Matlab. Since measured inputs are not needed, the process will be enabled on flexible structures and also inaccessible processes, for example the vibrations of a bridge under random excitation of traffic or wind. The extension of these tools to random excitation further broadens the applicability, and accommodates, for example, the turbulence loading on an airplane wing in the wind tunnel or during flight. The direct modal damping estimations of the SVMD are applicable to structures with larger damping than most current approaches. The project will support a doctoral student to learn state-variable modeling, random vibration, signal processing, and experimental instrumentation, in addition to course-work learning required in the doctoral program. Under-represented minorities, women, and economically disadvantaged students will be sought through the MSU Engineering Diversity Office. An undergraduate student will assist in setting up, instrumenting and running experiments. The PI will take part in an MSU summer program for middle schoolers, Mathematics Science and Technology (MST), by co-teaching a 'Mechanical Engineering' class.