Perturbation Methods for Nonlinear Control of Lagrangian Systems

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The principal goal of this proposed work is to develop proper orthogonal decomposition (POD) as a viable complementary alternative to conventional experimental modal analysis for vibration systems.Proper orthogonal decomposition has been used for obtaining "energy modes," as opposed to normal modes, from sensed system outputs. Proper orthogonal decomposition can indeed yield normal modes in lightly damped systems if the mass distribution is known. This research aims to overcome the requirement of a known mass distribution, estimate modal frequencies and damping factors and associate them with the correct mode, expand the applicability to arbitrary excitations, and compare the performance of POD with classical experimental modal analysis. Auxiliary objectives are the extension from 1-D distributed-parameter systems to 2-D systems, and the application of POD to multi-modal nonlinear responses. The research approach will involve theoretical analyses, numerical simulations, and experiments. Simulations and experiments will be used to test theoretical developments on simple systems with analytical solutions, and also on systems with complicated geometries. If POD were sufficiently developed, it would significantly enhance our ability to extract vibration parameters as a complement to traditional modal analysis. Experimental vibration facilities are globally prevalent, geared for industrial problems of noise, performance, and safety. Even if POD were used in a fraction of such laboratories, the total POD activity would be quite large. It will be particularly advantageous to systems for which sensed inputs are not available. The project is geared for a doctoral student's research program. The project will also involve an undergraduate researcher for applying POD and conventional modal analysis on experimental systems