Transactions of the Korean Society of Mechanical Engineers A (대한기계학회논문집A)

The Korean Society of Mechanical Engineers (대한기계학회)
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Modal Analysis Employing In-plane Strain of Cantilever Plates Undergoing Translational Acceleration

병진 가속을 받는 외팔 평판의 면내 변형률을 이용한 진동 해석

  • 유홍희 (한양대학교 기계공학부) ;
  • 임홍석 (한양대학교 대학원 기계설계학과)
  • Published : 2005.06.01
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Abstract

A modeling method for the modal analysis of cantilever plates undergoing in-plane translational acceleration is presented in this paper. Cartesian deformation variables are employed to derive the equations of motion and the resulting equations are transformed into dimensionless forms. To obtain the modal equation from the equations of motion, the in-plane equilibrium strain measures are substituted into the strain energy expression based on Von Karman strain measures. The effects of two dimensionless parameters (related to acceleration and aspect ratio) on the modal characteristics of accelerated plates are investigated through numerical studies.

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References

  1. Southwell, R. and Gough, F., 1921, 'The Free Transverse Vibration of Airscrew Blades,' British A.R.C. Reports and Memoranda, No. 766
  2. Theodorsen, T., 1935, 'Propeller Vibrations and the Effect of Centrifugal Force,' NASA TN, No. 516
  3. Schilhansl, M., 1958, 'Bending Frequency of a Rotating Cantilever Beam,' Transaction of ASME, Journal of Applied Mechanics, Vol. 25, pp. 28-30
  4. Putter, S. and Manor, H., 'Natural Frequencies of Radial Rotating Beams,' Journal of Sound and Vibration, Vol. 56, pp. 175-185, 1978 https://doi.org/10.1016/S0022-460X(78)80013-3
  5. Bhat, R., 'Transverse Vibrations of a Rotating Cantilever Beam with Tip Mass as Predicted by Using Beam Characteristic Orthogonal Polynomials in the Rayleigh-Ritz Method,' Journal of Sound and Vibration, Vol. 105, No.2, pp. 199-210,1986 https://doi.org/10.1016/0022-460X(86)90149-5
  6. Liew, K.M. and Lim, M.K., 1993, 'Transverse Vibration of Trapezoidal Plates of Variable Thickness: Symmetric Trapezoidals,' Journal of Sound and Vibration, Vol. 165, No. 1, pp. 45-67 https://doi.org/10.1006/jsvi.1993.1242
  7. Dokainish, M. and Rawtani, S., 1971, 'Vibration Analysis of Rotating Cantilever Plates,' International Journal for Numerical Methods in Engineering, Vol. 3, pp. 233-248 https://doi.org/10.1002/nme.1620030208
  8. Ramamurti, V. and Kielb, R., 1984, 'Natural Frequencies of Twisted Rotating Plates,' Journal of Sound and Vibration, Vol. 97, No. 3, pp. 429-449 https://doi.org/10.1016/0022-460X(84)90271-2
  9. Chihara, T., 1978, An Introduction to Orthogonal Polynomials, London: Gordon and Breach Science Publishers
  10. Leissa, A. W., 1969, Vibration of Plates, NASA SP-160
  11. Bhat, R., 1985, 'Natural Frequencies of Rectangular Plates Using Characteristic Orthogonal Polynomials In Rayleigh-Ritz Method,' Journal of Sound and Vibration, 102(4), pp. 493-499 https://doi.org/10.1016/S0022-460X(85)80109-7