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Vibration and stability of rotating and translating plates
Yang, Shih-Ming
Berkeley, Calif. : University of California, PhD dissertation, author retains copyright, 1988-04, PDF
The vibration and stability of a rotating circular plate that slides and tilts on the driving shaft is an important problem in machine dynamics. This work analyzes the vibration and response of a rotating and translating plate system with guides. Because of the clearance between the plate center hole and the shaft. the rotating plate can translate and tilt between the guide pair. The plate experiences large rigid body translation and tilting motions as well as flexible body elastic deformation. A constraint formulation is developed through the Lagrange multiplier technique to investigate the response of a rigid plate with guide located at different positions. A unified formulation of the equation of motion for systems with coupled rigid and flexible body motion is developed. This formulation predicts the natural frequencies and stability of the guided rotating and translating plate. There are two types of instability in linear gyroscopic systems: divergence and flutter. Divergence is a static instability. and flutter is a dynamic instability resulting in self-excited oscillation with increasing amplitude. A unified stability prediction method is developed to avoid case-by-case eigensolution calculations and provide a stability picture. Conditions on the coefficient matrices of the equation of motion are determined to ensure stability. A sufficient condition of flutter instability of linear gyroscopic systems is presented. A criterion guaranteeing asymptotic stability of nonconservative, linear gyroscopic systems is also derived.
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