DOI QR코드

DOI QR Code

Complex Modal Analysis of General Rotor System by Using Floquet Theory

플로케이론을 이용한 일반회전체의 복소 모드해석

  • 한동주 ((주)썬에어로시스 기술연구소) ;
  • 이종원 (한국과학기술원 기계공학과)
  • Published : 2005.10.01

Abstract

Based upon the Floquet theory, the complex modal solution for general rotor systems with periodically time-varying parameters is newly derived. The complete modal response can be obtained from the orthonormality condition between the time-variant eigenvectors and the corresponding adjoint vectors. The harmonic solutions such as the response and directional special a patterns are then derived in terms of harmonic modes whose coefficients are obtained from the modal analysis. The stability analysis by the Floquet's transition matrix and the eigen-analysis is also performed.

Keywords

References

  1. Lee, C. W., 1993, 'Vibration Analysis of Rotors,' Kluwer Academic Publishers
  2. Lee, C. W., 1991, 'A Complex Modal Testing Theory for Rotating Machinery,' Mechanical Systems and Signal Processing, Vol.5, No.2, pp. 119-137 https://doi.org/10.1016/0888-3270(91)90019-2
  3. Sinha, S. C., Pandiyan, R. and Bibb, J. S., 1996, 'Liapunov-Floquet Transformation: Computation and Applications to Periodic Systems,' Journal of Vibration and Acoustics, Vol. 118, pp. 209-217 https://doi.org/10.1115/1.2889651
  4. Robert, A. C., William, E., 1984, 'Control of Time-Periodic Systems,' J. GUIDANCE, Vol. 7, No.6, pp. 671-676 https://doi.org/10.2514/3.19911
  5. Genta, B., 1988, 'Whirling of Unsymmetrical Rotors: A Finite Element Approach Based on Complex Co-ordinates,' Journal of Sound and Vibration, Vol. 124(1), pp. 27-53 https://doi.org/10.1016/S0022-460X(88)81404-4
  6. Ardayfio, D. and Frohrib, D. A., 1976, 'Instability of an Asymmetric Rotor with Asymmetric Shaft Mounted on Symmetric Elastic Supports,' Journal of Engineering for Industry, pp. 1161-1165
  7. Meirovitch, 1970, 'Methods of Analytical Dynamics,' McGraw Hill
  8. Friedmann, P. and Hammond, C. E., 'Efficient Numerical Treatment of Periodic Systems with Application to Stability Problems, 1977,' International Journal for Numerical Methods in Engineering, Vol. 11, pp. 1117-1136 https://doi.org/10.1002/nme.1620110708
  9. Irrerier, H., 'Mathmatical Foundations of Experimental Modal Analysis in Rotor, 1993,' Mechanical Systems and Signal Processing, Vol. 13, No. 2, pp. 183-191 https://doi.org/10.1006/mssp.1998.1215
  10. Kramer E., 1993, 'Dynamics of Rotors and Foundations,' Springer-Verlag
  11. Weaver, J. and Gere, J. M., 1980, 'Matrix Analysis of Framed Structures,' D. Van Nostrand Company, Second Edition

Cited by

  1. Complex harmonic modal analysis of rotor systems vol.29, pp.7, 2015, https://doi.org/10.1007/s12206-015-0602-3