Transactions of the Korean Society for Noise and Vibration Engineering (한국소음진동공학회논문집)

The Korean Society for Noise and Vibration Engineering (한국소음진동공학회)
권호 표지
DOI QR코드

DOI QR Code

In-plane Natural Vibration Analysis of a Rotating Annular Disk

회전하는 환상 디스크의 면내 고유진동 해석

  • 송승관 (인하대학교 대학원 기계공학과) ;
  • 곽동희 (인하대학교 대학원 기계공학과) ;
  • 김창부 (인하대학교 공과대학 기계공학부)
  • Published : 2009.02.20
Download PDF
⟨ Previous Next ⟩

Abstract

In this paper, we present the equations of motion by which the natural vibration of a rotating annular disk can be analyzed accurately. These equations are derived from the theory of finite deformation and the principle of virtual work. The radial displacements of annular disk at the steady state where the disk is rotating at a constant angular velocity are determined by non-linear static equations formulated with 1-dimensional finite elements in radial direction. The linearlized equations of the in-plane vibrations at the disturbed state are also formulated with 1-dimensional finite elements in radial direction along the number of nodal diameters. They are expressed as in functions of the radial displacements at the steady state and the disturbed displacements about the steady state. In-plane static deformation modes of an annular disk are used as the displacement functions for the interpolation functions of the 1-dimensional finite elements. The natural vibrations of an annular disk with different boundary conditions are analyzed by using the presented model and the 3-dimensional finite element model to verify accuracy of the presented equations of motion. Its results are compared and discussed.

Keywords

References

  1. Leissa, A. W., 1969, “Vibration of Plates,” NASA SP-160, Office of Technology Utilization, NASA, Reproduced by National Technical Information Service, U.S. Department of Commerce
  2. Leissa, A. W., 1977, “Recent Research in Plate Vibrations : Classical Theory,” Shock and Vibration Digest, Vol. 9, No. 10, pp. 13-24 https://doi.org/10.1177/058310247700901005
  3. Leissa, A. W., 1978, “Recent Research in Plate Vibrations : Complicating Effects,” Shock and Vibration Digest, Vol. 10, No. 12, pp. 21-35 https://doi.org/10.1177/058310247801001204
  4. Leissa, A. W., 1981, “Plate Vibration Research, 1976-1980 : Classical Theory,” Shock and Vibration Digest, Vol. 13, No. 9, pp. 11-22 https://doi.org/10.1177/058310248101300905
  5. Leissa, A. W., 1981, “Plate Vibration Research, 1976-1980 : Complicating Effects,” Shock and Vibration Digest, Vol. 13, No. 10, pp. 19-36
  6. Leissa, A. W., 1987, “Recent Studies in Plate Vibrations, 1981-85 : Part I. Classical Theory,” Shock and Vibration Digest, Vol. 19, No. 2, pp. 11-18 https://doi.org/10.1177/058310248701900204
  7. Leissa, A. W., 1987, “Recent Studies in Plate Vibrations, 1981-85 : Part II. Complicating Effects,” Shock and Vibration Digest, Vol. 19, No. 3, pp. 10-24 https://doi.org/10.1177/058310248701900304
  8. Irie, T., Yamada, G. and Muramoto, Y., 1984, “Natural Frequencies of In-plane Vibration of Annular Plates,” Journal of Sound and Vibration, Vol. 97, No. 1, pp. 171-174 https://doi.org/10.1016/0022-460X(84)90479-6
  9. Chen, J. S. and Jhu, J. L., 1996, “On the In-plane Vibration and Stability of a Spinning Annular Disk,” Journal of Sound and Vibration, Vol. 195, No. 4, pp. 585-593 https://doi.org/10.1006/jsvi.1996.0447
  10. Farag, N. H. and Pan, J., 2003, “Modal Characteristics of In-plane Vibration of Circular Plates Clamped at the Outer Edge,” Journal of the Acoustical Society of America, Vol. 113, No. 4, pp. 1935-1946 https://doi.org/10.1121/1.1553456
  11. Deshpande, M. and Mote Jr., C. D., 2003, “In-plane Vibrations of a Thin Rotating Disk,” Journal of Vibration and Acoustics, Transactions of the ASME, Vol. 125, No. 1, pp. 68-72 https://doi.org/10.1115/1.1522419
  12. Park, C. I., 2008, “Frequency Equation for the In-plane Vibration of a Clamped Circular Plate,” Journal of Sound and Vibration, Vol. 313, No. 1-2, pp. 325-333 https://doi.org/10.1016/j.jsv.2007.11.034
  13. Srinivasan, V. and Ramamurti, V., 1980, “Inplane Vibrations of Annular Disk Using Finite Elements,” Journal of Mechanical Design, Transactions of the ASME, Vol. 102, pp. 585-588 https://doi.org/10.1115/1.3254789
  14. Kim, C. B. and Shim, S. S., 1998, “A Method for Finite Element Analysis of Rotating Structures with Cyclic Symmetry,” Transactions of the Korean Society for Noise and Vibration Engineering, Vol. 8, No. 6, pp. 1150-1157