Combination Resonance of Nonlinear Rotating Balanced Shafts Subjected to Periodic Axial Load

Subject Areas : Engineering

M.S Qaderi ¹ , S.A.A Hosseini ² , M Zamanian ³

1 - Department of Mechanical Engineering, Faculty of Engineering, Kharazmi University, Tehran, Iran
2 - Department of Mechanical Engineering, Faculty of Engineering, Kharazmi University, Tehran, Iran
3 - Department of Mechanical Engineering, Faculty of Engineering, Kharazmi University, Tehran, Iran

Received: 2018-01-21 Accepted : 2018-03-23 Published : 2018-06-30

Keywords:

References:

[1] Chen L. W., Ku D. M., 1990, Dynamic stability analysis of a rotating shaft by the finite element method, Journal of Sound and Vibration 143(1): 143-151.
[2] Lee H. P., Tan T. H., Leng G. S. B., 1997, Dynamic stability of spinning timoshenko shafts with a time-dependent spin rate, Journal of Sound and Vibration 199(3): 401-415.
[3] Sheu H.C., Chen L.W., 2000, A lumped mass model for parametric instability analysis of cantilever shaft–disk systems, Journal of Sound and Vibration 234(2): 331-348.
[4] Pei Y.C., 2009, Stability boundaries of a spinning rotor with parametrically excited gyroscopic system, European Journal of Mechanics - A/Solids 28(4): 891-896.
[5] Bartylla D., 2012, Stability investigation of rotors with periodic axial force, Mechanism and Machine Theory 58: 13-19.
[6] Mailybaev A. A., Seyranian A. P., 2013, Instability of a general rotating system with small axial asymmetry and damping, Journal of Sound and Vibration 332(2): 346-360.
[7] Mailybaev A. A., Spelsberg-Korspeter G., 2015, Combined effect of spatially fixed and rotating asymmetries on stability of a rotor, Journal of Sound and Vibration 336: 227-239.
[8] Bolotin V.V., 1964, The Dynamic Stability of Elastic System , Holden-day, Sanfransico, CA.
[9] Yamamoto T., Ishida Y., Aizawa K., 1979, On the subharmonic oscillations of unsymmetrical shafts, Bulletin of JSME 22(164): 164-173.
[10] Yamamoto T., Ishida Y., Ikeda T., 1981, Summed-and-differential harmonic oscillations of an unsymmetrical shaft, Bulletin of JSME 24(187): 183-191.
[11] Yamamoto T., Ishida Y., Ikeda T., Yamada M.,1981, Subharmonic and summed-and-differential harmonic oscillations of an unsymmetrical rotor, Bulletin of JSME 24(187): 192-199.
[12] Yamamoto T., Ishida Y., Ikeda T., Suzuki H., 1982, Super-summed-and-differential harmonic oscillations of an unsymmetrical shaft and an unsymmetrical rotor, Bulletin of JSME 25(200): 257-264.
[13] Yamamoto T., Ishida Y., Ikeda T., Yamamoto M., 1982, Nonlinear forced oscillations of a rotating shaft carrying an unsymmetrical rotor at the major critical speed, Bulletin of JSME 25(210): 1969-1976.
[14] Yamamoto T., Ishida Y., Ikeda T., 1983,Vibrations of a rotating shaft with rotating nonlinear restoring forces at the major critical speed, Transactions of the Japan Society of Mechanical Engineers Series C 49(448): 2133-2140.
[15] Ishida Y., Ikeda T., Yamamoto T., 1986, Effects of nonlinear spring characteristics on the dynamic unstable region of an unsymmetrical rotor, Bulletin of JSME 29(247): 200-207.
[16] Ishida Y., Liu J., Inoue T., Suzuki A., 2008,Vibrations of an asymmetrical shaft with gravity and nonlinear spring characteristics (Isolated Resonances and Internal Resonances), Journal of Vibration and Acoustics 130: 041004.
[17] Shahgholi M., Khadem S. E., 2012, Primary and parametric resonances of asymmetrical rotating shafts with stretching nonlinearity, Mechanism and Machine Theory 51: 131-144.
[18] Shahgholi M., Khadem S.E., Bab S., 2015, Nonlinear vibration analysis of a spinning shaft with multi-disks, Meccanica 50: 2293-2307.
[19] Ghorbanpour Arani A., Haghparast E., Amir S., 2012, Analytical solution for electro-mechanical behavior of piezoelectric rotating shaft reinforced by BNNTs under nonaxisymmetric internal pressure, Journal of Solid Mechanics 4: 339-354.
[20] Hosseini S. A. A., Zamanian M., 2013, Multiple scales solution for free vibrations of a rotating shaft with stretching nonlinearity, Scientia Iranica 20(1): 131-140.
[21] Ishida Y., Nagasaka I., Inoue T., Lee S., 1996, Forced oscillations of a vertical continuous rotor with geometric nonlinearity, Nonlinear Dynamics 11(2): 107-120.
[22] Nayfeh A.H., Pai P.F., 2004, Linear and Nonlinear Structural Mechanics, Wiley, New York.
[23] Nayfeh A. H.,1981, Introduction to Perturbation Techniques, Wiley, New York.
[24] Nayfeh A. H., Mook D. T., 1979, Nonlinear Oscillations, Wiley, New York.
[25] Valeev K. G., 1963, On the danger of combination resonances, Journal of Applied Mathematics and Mechanics 27(6): 1745-1759.