Vibration analysis and robust control of highly deformable beams in a heavy pinched loop configuration
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A heavy pinched loop is formed by bringing and clamping the two ends of a highly deformable slender beam, elastica. A collocation solution technique is implemented for studying the formation statically and dynamically, i.e. small vibrations around the large deformed static solutions, and the earlier work using a shooting method is validated. A new and clear Galerkin formulation capable of modelling damping is established for finding transients, and a new theoretical multi-point boundary value problem approach is used for numerically obtaining the frequency response function. Lastly, the obtained dynamic model is used for active vibration control, wherein a controller is designed using H∞ algorithm for active damping in a heavy pinched loop for two simplified cases, and the simulated results are shown.
Mathematics Subject Classification74B20 74H45 93C05 65L15
KeywordsElastica Pinched loop Collocation Frequency response function Robust control
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