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

The Korean Society for Noise and Vibration Engineering (한국소음진동공학회)
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Three-dimensional Vibration Analysis of Circular Rings with an Elliptical or Circular Cross-section

타원형 또는 원형 단면을 가진 원형 링의 3차원적 진동해석

  • 심현주 (중앙대학교 일반대학원 건축학과) ;
  • 우하영 (중앙대학교 일반대학원 건축학과) ;
  • 강재훈 (중앙대학교 공과대학 건축공학과)
  • Published : 2006.10.20
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Abstract

A three-dimensional (3-D) method of analysis is presented for determining the free vibration frequencies and mode shapes of thick, complete (circumferentially closed), circular rings with an elliptical or circular cross-section. Displacement components $u_r,\;u_\theta\;and\;u_z$ in the radial, circumferential, and axial directions, respectively, are taken to be periodic in ${\theta}$ and in time, and algebraic polynomials in the r and z directions. Potential (strain) and kinetic energies of the circular rings are formulated, and upper bound values of the frequencies are obtained by minimizing the frequencies. As the degree of the polynomials is increased, frequencies converge to the exact values. Convergence to four-digit exactitude is demonstrated for the first five frequencies of the rings. Novel numerical results are presented for the circular rings having an elliptical cross-section based upon 3-D theory. Comparisons are also made between the frequencies from the present 3-D Ritz method and ones obtained from thin and thick ring theories, experiments, and another 3-D method.

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References

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