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Paper Count: 30121
Linear Dynamic Stability Analysis of a Continuous Rotor-Disk-Blades System
Abstract:Nowadays, using rotating systems like shafts and disks in industrial machines have been increased constantly. Dynamic stability is one of the most important factors in designing rotating systems. In this study, linear frequencies and stability of a coupled continuous flexible rotor-disk-blades system are studied. The Euler-Bernoulli beam theory is utilized to model the blade and shaft. The equations of motion are extracted using the extended Hamilton principle. The equations of motion have been simplified using the Coleman and complex transformations method. The natural frequencies of the linear part of the system are extracted, and the effects of various system parameters on the natural frequencies and decay rates (stability condition) are clarified. It can be seen that the centrifugal stiffening effect applied to the blades is the most important parameter for stability of the considered rotating system. This result highlights the importance of considering this stiffing effect in blades equation.
Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1126593Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1104
 C. W. Chang-Jian, C. K. Chen, “Chaotic response and bifurcation analysis of a flexible rotor supported by porous and non-porous bearings with nonlinear suspension,” Nonlinear Analysis: Real World Applications, 10 (2009) 1114–1138.
 C. W. Chang-Jian, C. K. Chen, “Chaos and bifurcation of a flexible rub-impact rotor supported by oil film bearings with nonlinear suspension,” Mechanism and Machine Theory, 42 (2007) 312–333.
 C. W. Chang-Jian, C. K. Chen, “Chaos of rub–impact rotor supported by bearings with nonlinear suspension,” Tribology International, 42 (2009) 426–439.
 Sanches L, Michon G, Berlioz A, Alazard D, “Instability zones for isotropic and anisotropic multibladed rotor configurations,” Mechanism and Machine Theory, 46 (2011) 1054–1065.
 Santos IF, Saracho CM, Smith JT, Eiland J, “Contribution to experimental validation of linear and non-linear dynamic models for representing rotor–blade parametric coupled vibrations,” Journal of Sound and Vibration, 271 (2004) 883–904.
 C. W. Chang-Jian, “Bifurcation and chaos of gear-rotor–bearing system lubricated with couple-stress fluid,” Nonlinear Dynamic, 79(1) (2015) 749-763.
 S. E. Khadem, M. Shahgholi, S. A. A. Hosseini, “Primary resonances of a nonlinear in-extensional rotating shaft,” Mechanism and Machine Theory, 45 (2010) 1067–1081.
 S. E. Khadem, M. Shahgholi, S. A. A. Hosseini, “Two-mode combination resonances of an in-extensional rotating shaft with large amplitude,” Nonlinear Dynamic, 65 (2011) 217–233.
 Shahgholi M, Khadem S. E. and Bab S., “Free vibration analysis of a nonlinear slender rotating shaft with simply support conditions,” Mechanism and Machine Theory, 82 (2014) 128-140.
 Shahgholi M, Khadem S. E. and Bab S., “Nonlinear vibration analysis of a spinning shaft with multi-disks,” Meccanica, 50(9) (2015) 2293-2307.
 S. Yan, E. H. Dowell, B. Lin, “Effects of nonlinear damping suspension on nonperiodic motions of a flexible rotor in journal bearings,” Nonlinear Dynamic, 78(2) (2014) 1435-1450.
 L. Wang, D. Q. Cao, W. Huang, “Nonlinear coupled dynamics of flexible blade–rotor–bearing systems,” Tribology International, 43 (2010) 759–778.
 D. Zou, Z. Rao, N. Ta, “Coupled longitudinal-transverse dynamics of a marine propulsion shafting under superharmonic resonances,” Journal of Sound and Vibration, 346 (2015) 248–264.
 Genta, G., “On the stability of rotating blade arrays,” Journal of Sound and Vibration, 273(4–5) (2004) 805-836.
 Nayfeh, A. H. and P. F. Pai, “Linear and nonlinear structural mechanics,” 2004, New York: Wiley-Interscience.
 Nayfeh, A. H., “Introduction to perturbation techniques,” 2011, John Wiley & Sons.
 Staino A., B. Basu, and S. R. K. Nielsen, “Actuator control of edgewise vibrations in wind turbine blades,” Journal of Sound and Vibration, 2012. 331(6): p. 1233-1256.
 L. Meirovitch, “Fundamentals of Vibrations,” McGraw Hill, New York, 2001.
 Parviz Ghadimi, Hadi Paselar Bandari, Ali Bankhshandeh Rostami, “Determination of the heave and pitch motions of a floating cylinder by analytical solution of its diffraction problem and examination of the effects of geometric parameters on its dynamics in regular waves,” International Journal of Applied Mathematical Research, 1(4) (2012) 611-633.
 S. W. Shaw, B. Geist, “Tuning for performance and stability in systems of nearly Tautochronic torsional vibration absorbers,” J. Vibr. Acoust, 132 (2010) 041005 (-1).
 W Thomson, “Theory of Vibration with Applications,” GEORGE ALLEN & UNWIN, London, 1981.
 G. Genta, “Dynamics of Rotating Systems,” springer, (2005).