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

  • 제12권12호
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  • Pages.970-978
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  • 2002
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  • 1598-2785(pISSN)
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  • 2287-5476(eISSN)
한국소음진동공학회 (The Korean Society for Noise and Vibration Engineering)
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직교좌표계에 의한 아치의 자유진동

Free Vibrations of Arches in Cartesian Coordinates

  • Lee, Byoung-Koo (School of Architectural Engineering, Wonkwang University) ;
  • Lee, Yong-Soo (Department of Architectural Interior Design, Chongin University) ;
  • Kim, Il-Jung (Graduate School, Wonkwang University) ;
  • Choi, Kou-Moon (School of Civil and Environmental Engineering, Wonkwang University)
  • 발행 : 2002.12.01
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⟨ 이전 논문 다음 논문 ⟩

초록

이제까지 아치의 자유진동에 관한 연구들은 모두 극좌표계에서 해석한 연구들이다. 이 논문은 극좌표계에서 아치의 해석을 지양하고, 직교좌표계에서 아치의 자유진동을 해석한 연구이다. 아치의 자유진동을 지배하는 미분방정식을 직교좌표계에서 유도하고. 이를 수치해석하여 고유진동수와와 진동형을 산출하였다. 미분방정식에는 회전관성 효과를 고려하고. 아치의 선형은 포물선으로 채택하였다. 실제 구조물에 대한 적용을 위하여 비대칭 축을 갖는 아치를 수치해석 하였다. 본 연구와 SAP 2000의 결과를 비교하여 본 연구의 타당성을 검증하였다. 수치해석의 결과로 아치의 무차원 변수들이 무차원 고유진동수에 미치는 영향을 분석하고. 전형적인 진동형의 예를 그림에 나타내었다.

The differential equations governing free vibrations of the elastic arches with unsymmetric axis are derived in Cartesian coordinates rather than in polar coordinates. in which the effect of rotatory inertia is included. Frequencies and mode shapes are computed numerically for parabolic arches with both clamped ends and both hinged ends. Comparisons of natural frequencies between this study and SAP 2000 are made to validate theories and numerical methods developed herein. The convergent efficiency is highly improved under the newly derived differential equations in Cartesian coordinates. The lowest four natural frequency parameters are reported, with and without the rotatory inertia, as functions of three non-dimensional system parameters the rise to chord length ratio. the span length to chord length ratio, and the slenderness ratio. Also typical mode shapes of vibrating arches are presented.

키워드

참고문헌

  1. Lee, B. K. and Wilson, J. F., 1989. 'Free Vibrations of Arches with Variable Curvature.' journal of Sound and Vibration, Vol. 136, No. 1, op. 75-89 https://doi.org/10.1016/0022-460X(90)90939-W
  2. Romanelli, E. and Laura. P. A. A., 1972, Fundamental Frequency of Non-drcular, Elastic, Hinged Arcs.' Journal of Sound and Vibration. Vol. 24, No. 1. pp. 17-22 https://doi.org/10.1016/0022-460X(72)90118-6
  3. Wang, T. M.. 1972, 'Lowest Natural Frequency of damped Parabolic Arcs.' Journal of the Structural Division, ASCE, Vol. 98, No. STl, pp. 407-411
  4. Wang. T. M. and Moore, J. A., 1973. 'Lowest Natural Extensional Frequency of Clamped Elliptic Arcs.' Journal of Sound and Vibration. Vol. 30, No. 1, pp. 1-7 https://doi.org/10.1016/S0022-460X(73)80046-X
  5. Wolf, Jr. J.A., 1971, 'Natural Frequencies of Circular Arches' Journal of the Structural Division, ASCE. Vol. 97. No. ST9, pp. 2337-2350
  6. Veletsos. A. S., Austin, A. J., Pereira, C. A. L. and Wung, S. J., 1972. 'Free In-plane Vibrations of Circular Arches.' Journal of Engineering Mechanics Division, ASCE. Vol. 93, pp. 311-329
  7. Kang. K. and Bert, C. W., 1995, 'Vibration Analyses of Shear Deformable Circular Arches by the Differential Quadrature Method.' Journal of Sound and Vibration, Vol. 181, pp. 353-360
  8. 이병구, 이용수, 오상진, 2002, '변단면 변화곡 률 캔틸레버 아치의 자유진동' 한국소음진동공학회논문집, 제 10권, 제 2호, pp. 353-360
  9. Oh, S. J.. Lee. B. K. and Lee. I. W., 2000, 'Free Vibrations of Non-circular Arches with Non-uniform Cross-section.' International Journal of Solids and Structures, Vol. 37, No. 36. pp. 4871-4891 https://doi.org/10.1016/S0020-7683(99)00194-8
  10. Irie, T. and Yamada, G. and Tanaka, K., 1983, 'Natural Frequencies of In-plane Vibration of Arcs.' Journal of Applied Mechanics, ASME. Vol. 50, pp. 449-4527 https://doi.org/10.1115/1.3167058
  11. Davis, R., Henshell, R.D. and Warburton, G. B., 1972, 'Constant Curvature Beam Finite Elements for In-plane Vibration.' Journal of Sound and Vibration, Vol. 25, No. 4, pp. 561-576 https://doi.org/10.1016/0022-460X(72)90478-6
  12. Wilson, J. F. and Lee, B. K., 1995, 'In-plane Free Vibrations of Catenary Arches with Unsymmetric Axis.' Structural Engineering and Mechanics, An International Journal, Vol. 3. No. 5,pp. 511-525
  13. Borg and Gennaro, 1957, Advanced Structural Analysis. McGrow-Hill Book Company
  14. Lee. B. K.. Oh. S. J. and Park. K. K., 2002, 'Free Vibrations of Shear Deformable Circular Curved Beams Resting on an Elastic Foundation' International Journal of Structural Stability and Dynamics. Vol. 2, No. 1. pp. 77-97 https://doi.org/10.1142/S0219455402000440
  15. Al-Khafaji. A. W. and Tooley, J. R., 1986. Numerical Method in Engineering Practice, Holt, Reinhardt and Winston, Inc
  16. Oh, S. J., 1996. Free Vibrations of Arches with Vahable Cross-section, Ph. D. Thesis, Wonkwang University