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Analytical study of the dynamic behavior of geometrically nonlinear shaft-disk rotor systems

Published online by Cambridge University Press:  06 January 2012

Muhammad Rizwan Shad
Affiliation:
Universitéde Toulouse, ICA, INSA, 135 Av. de Rangueil, 31077 Toulouse, France
Guilhem Michon
Affiliation:
Université de Toulouse, ICA, ISAE, 10 Av. Édouard Belin, 31055 Toulouse, France
Alain Berlioz
Affiliation:
Université de Toulouse, ICA, UPS, 118 route de Narbonne, 31062 Toulouse, France
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Abstract

This paper explores analytically the nonlinear dynamic behavior of rotors. Coupled nonlinear equations of motion are formulated using Hamilton’s principle. The rotor model is composed of a rigid disk and a flexible shaft which is characterized as a beam of circular cross section. Various influences are taken into account like the effect of higher order large deformations, rotary inertia, gyroscopic effect, rotor unbalance and the effect of a dynamic axial force. Forced response due to a mass unbalance is presented first for the linear analysis and then perturbation techniques are used to solve the complete equations of motion including nonlinear terms. Method of multiple scales is applied to examine the nonlinear behaviour of the rotor system. Resonant curves are plotted for different possible resonance conditions. It is concluded that the higher order large deformations and axial force acting dynamically on the rotor have a significant effect on its nonlinear response. This response varies for different parameters of the rotor like an unbalance mass and diameter of the shaft.

Type
Research Article
Copyright
© AFM, EDP Sciences 2011

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