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Shape Optimization of a Rotating Cantilever Beam Considering Its Modal and Stress Characteristics

회전 외팔보의 진동 및 응력 특성을 고려한 형상 최적화

  • Published : 2001.04.01

Abstract

It is well known that natural frequencies increase when a cantilever beam rotates about the axis perpendicular to its longitudinal axis. Such phenomena that are caused by centrifugal inertia forces are often referred to as the stiffening effects. Occasionally it is necessary to control the variation of a natural frequency or the maximum stress of a rotating beam. By changing the thickness of the rotating beam, the modal or the stress characteristics can be changed. The thickness of the rotating beam is assumed to be a cubic spline function in the present work. An optimization method is employed to find the optimal thickness shape of the rotating beam. This method can be utilized for the design of rotating structures such as turbine blades and aircraft rotary wings.

Keywords

Cantilever Beam;Rotating Angular Speed;Modal Analysis;Natural Frequency Variation;Stress Distribution;Shape Optimization

References

  1. 최창민, 유홍희, 양현익, 2000, '회전 외팔보의 과도상태 진동시 발생하는 응력 분포 연구,' 한국 소음진동공학회지, 제10권, 제2호, pp. 306-311
  2. Vanderplaats, G. N., 1985, ADS Manual, Engineering Design Optimization Inc., Santa Barbara
  3. Yoo, H. and Shin, S., 1998, 'Vibration Analysis of Rotating Cantilever Beams,' J. of Sound and Vibration, Vol. 212, No. 5, pp. 807-828 https://doi.org/10.1006/jsvi.1997.1469
  4. Kane, T. and Levinson, D., 1985, Dynamics: Theory and Applications, McGraw-Hill Book Co., New York, N. Y.
  5. 유홍희, 1992, '회전 외팔보의 굽힘 진동해석,' 대한기계학회, 제16권, 제5호, pp. 891-898
  6. Kane, T., Ryan, R. and Banerjee, A., 1987, 'Dynamics of Cantilever Beam Attached to a Moving Base,' J. Guidance, Control, and Dynamics, Vol. 10, pp. 139-151
  7. Yoo, H., Ryan, R. and Scott, R., 1995, 'Dynamics of Flexible Beams Undergoing Overall Motions,' J. of Sound and Vibration, Vol. 181, No. 2, pp. 261-278 https://doi.org/10.1006/jsvi.1995.0139
  8. Carnegie, W., 1959, 'Vibrations of Rotating Cantilever Blading: Theoretical Approaches to the Frequency Problem Based on Energy Methods,' J. Mechanical Engineering Sci., Vol. 1, pp. 235-240 https://doi.org/10.1243/JMES_JOUR_1959_001_028_02
  9. Yntema, R., 1955, 'Simplified Procedures and Charts for the Rapid Estimation of Bending Frequencies of Rotating Beams,' NACA 3459
  10. Putter, S. and Manor, H., 1978, 'Natural Frequencies of Radial Rotating Beams,' J. Sound and Vibration, Vol. 56, pp. 175-185 https://doi.org/10.1016/S0022-460X(78)80013-3
  11. Southwell, R. and Gough, F., 1921, 'The Free Transverse Vibration of Airscrew Blades,' British A. R. C. Reports and Memoranda No.766
  12. Schilhansl, M., 1958, 'Bending Frequency of a Rotating Cantilever Beam,' J. of Appl. Mech. Trans. Am. Soc. Mech. Engrs, Vol. 25, pp. 28-30