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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 ,
Guilhem Michon  and
Alain Berlioz
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
*
aCorresponding author: [email protected]
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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.

Keywords

Rotordynamicsnonlinearlarge deformations in bendingmethod of multiple scalesresonant curvesDynamique des rotorsnon-linéairegrandes déformations en flexionméthode des echelles multiplescourbes de résonance
Type
Research Article
Information
Mechanics & Industry , Volume 12 , Issue 6 , 2011 , pp. 433 - 443
Copyright
© AFM, EDP Sciences 2011

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References

J.S. Rao, Rotordynamics, 3rd edition, New Age International, India, 1996, p. 420, ISBN 8122409776
M. Lalanne, G. Ferraris, Rotordynamics prediction in engineering, 2nd edition, John Wiley & sons, 1998, p. 266, ISBN 9780471972884
L.M. Adams, Rotating machinery vibrations from analysis to troubleshooting, Marcel Dekker Inc, New York, 2001, p. 354, ISBN 9780824702588
T. Yamamoto, Y. Ishida, Linear and nonlinear rotordynamics: a modern treatment with applications, Wiley Series in Nonlinear Science, 2001, p. 348, ISBN: 978-0471181750
A. Muszynska, Rotordynamics, Taylor & Francis, 2005, p. 1075, ISBN 9780824723996
G. Genta, Dynamics of rotating systems, Springer, New York, 2005, p. 685, ISBN 9780387209364
J. Kicinski, Rotor dynamics, 2nd ed., IFFM Publishers, Gdansk, 2006, p. 539, ISBN 8372045429
W. Batko, Z. Da¸browski, J. Kiciñski, Nonlinear effects in technical diagnostics, Polish Academy of Science, Warsaw, 2008, p. 303, ISBN 9788372047489
Ehrich, F., Observations of nonlinear phenomena in rotordynamics, J. Syst. Design Dyn. 2 (2008) 641–651 CrossRefGoogle Scholar
Ishida, Y., Nagasaka, I., Inoue, T., Lee, S., Forced oscillations of a vertical continuous rotor with geometric nonlinearity, Nonlinear Dynamics 11 (1996) 107–120 CrossRefGoogle Scholar
Duchemin, M., Berlioz, A., Ferraris, G., Dynamic behavior and stability of a rotor under base excitations, ASME J. Vib. Acoustics 128 (2006) 576–585 CrossRefGoogle Scholar
Driot, N., Lamarque, C.H., Berlioz, A., Theoretical and experimental analysis of a base excited rotor, ASME J. Comput. Nonlinear Dyn. 1 (2006) 257–263 CrossRefGoogle Scholar
M. Géradin, D. Rixen, Mechanical vibrations – Theory and application to structural dynamics, John Wiley & Sons, 2nd ed., 1997, p. 425, ISBN 9780471975243
A.H. Nayfeh, D.T. Mook, Nonlinear oscillations, Wiley and Sons, New York, 2007, p. 704, ISBN 9780471121428
Nayfeh, A.H., Pai, P., Linear and nonlinear structural mechanics, Wiley and Sons, New York, 2004, p. 746, ISBN 9780471593560
Michon, G., Manin, L., Parker, R.G., Dufour, R., Duffing oscillator with parametric excitation: analytical and experimental investigation on a belt-pulley system, ASME J. Computational Nonlinear Dynamics 3 (2008) 031001–1 CrossRefGoogle Scholar
Yabuno, H., Kunitho, Y., Inoue, T., Ishida, Y., Nonlinear analysis of rotor dynamics by using method of multiple scales, IUTAM Symposium on Dynamics and Control of Nonlinear Systems with Uncertainty 2 (2007) 167–176 CrossRefGoogle Scholar
Shad, R., Michon, G., Berlioz, A., Modeling and analysis of nonlinear rotordynamics due to high order deformation in bending, J. Appl. Math. Modeling 35 (2011) 2145–2159 CrossRefGoogle Scholar
Hosseini, S., Khadem, S., Free vibration analysis of a rotating shaft with nonlinearities in curvature and inertia, Mech. Mach. Theory 44 (2009) 272–288 CrossRefGoogle Scholar