Journal of the Computational Structural Engineering Institute of Korea (한국전산구조공학회논문집)

Computational Structural Engineering Institute of Korea (한국전산구조공학회)
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Lowest Symmetrical and Antisymmetrical Natural Frequencies of Shallow Arches on Two-Parameter Elastic Foundations

두 개의 매개변수로 표현되는 탄성지반 위에 놓인 낮은 아치의 최저차 대칭 및 역대칭 고유진동수

  • Published : 2002.06.01
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Abstract

This paper deals with the free vibrations of shallow arches resting on elastic foundations. Foundations we assumed to follow the hypothesis proposed by Pasternak. The governing differential equation is derived for the in-plane free vibration of linearly elastic arches of uniform stiffness and constant mass per unit length. Two arch shapes with hinged-hinged and clamped-clamped end constraints we considered in analysis. The frequency equations (lowest symmetrical and antisymmetrical frequency equations) we obtained by Galerkin's method. The effects of arch rise, Winkler foundation parameter and shear foundation parameter on the lowest two natural frequencies are investigated. The effect of initial arch shapes on frequencies is also studied.

이 논문은 탄성지반 위에 놓인 낮은 아치의 자유진동에 관한 연구이다. Pasternak가 제안한 두 개의 매개변수로 표현되는 지반모형을 채택하여 대상아치의 자유진동을 지배하는 미분방정식을 유도하였다. 양단회전 및 양단고정의 단부 조건을 갖는 두 종류의 아치선형을 유도된 지배방정식에 적용하여 Galerkin method로 해석함으로써 최저차 대칭 및 역대칭 고유진동수 방정식을 산출하였다 아치높이, Winkler지반계수 및 전단지반계수가 고유진동수에 미치는 영향을 분석하였으며, 아치선형이 고유진동수에 미치는 영향을 분석하였다.

Keywords

References

  1. S. Kukla, 'Free Vibration of a Beam Support on a Stepped Elastic Foundation' Journal of Sound and Vibration, Vol. 149, 1991, pp.259-265 https://doi.org/10.1016/0022-460X(91)90635-W
  2. 이병구, '전단층을 갖는 탄성지반위에 놓인 보의 자유진동 해석', 한국강구조학회 논문집, 제6권 제3호, 1994, pp.107-115
  3. T. Yokoyama, 'Vibration Analysis of Timoshenko Beam-Columns on Two-Parameter Elastic Foundations,' Computers and Structures, Vol. 61, 1996, pp.995-1007 https://doi.org/10.1016/0045-7949(96)00107-1
  4. M. A. De Rosa and M. J. Maurizi, 'The Influence of Concentrated Masses and Pasternak Soil on the Free Vibrations of Euler Beams-Exact Solution,' Journal of Sound and Vibration, Vol. 212, 1998, pp.573-581 https://doi.org/10.1006/jsvi.1997.1424
  5. 신영재, 김재호, 황정기, 'Differential Transformation에 의한 가변 2 파라미터 탄성기초에 설치된 보의 진동해석', 한국소음진동공학회 논문집, 제11권, 제8호, 2001, pp.357-363
  6. P. A. A. Laura and M. J. Maurizi, 'Recent Research on Vibrations of Arch-Type Structures,' The Shock and Vibration Digest, Vol. 19, 1987, pp.6-9
  7. E. Volterra, 'Bending of Circular Beam Resting on an Elastic Foundation,' Journal of Applied Mechanics, ASME, Vol. 19, 1952, pp.1-4
  8. E. Volterra, 'Deflection of Circular Beams Resting on an Elastic Foundation obtained by the method of Harmonic Analysis,' Journal of Applied Mechanics, ASME, Vol. 20, 1953, pp.227-237
  9. D. E. Panayotounakos and P. S. Theocaris, 'Circular Beam on Elastic Foundation,' Journal of Engineering Mechanics Division, ASCE, Vol. 105, 1979, pp.839-853
  10. E. Volterra and J. H. Gains, Advanced Strength of Materials, Prentice-Hall, 1971
  11. D. E. Panayotounakos and P. S. Theocaris, 'The Dynamically Loaded Circular Beam on an Elastic Foundation,' Journal of Applied Mechanics, ASME, Vol. 47, 1980, pp.139-144
  12. T. M. Wang and W. F. Brannen, 'Natural Frequencies for Out-of-Plane Vibrations of Curved Beams on Elastic Foundations,' Journal of Sound and Vibration, Vol. 84, 1982, pp.241-246
  13. M. S. Issa, 'Natural Frequencies of Continuous Curved Beams on Winkler-Type Foundation,' Journal of Sound and Vibration, Vol. 127, 1988, pp.291-301 https://doi.org/10.1016/0022-460X(88)90304-5
  14. 이병구, 오상진, 이재만, '탄성지반위에 놓인 곡선형 Timoshenko보의 자유진동', 한국전산구조공학회 논문집, 제11권, 제2호, 1998, pp.273-280
  15. 이병구, 박광규, 오상진, '두 개의 매개변수로 표현되는 탄성지반위에 놓인 원호형 곡선보의 자유진동', 한국전산구조공학회 논문집, 제12권 제4호, 1999, pp.661-669
  16. G. J. Simitses, 'Snapping of Low Pinned Arches on an Elastic Foundation,' Journal of Applied Mechanics, ASME, Vol. 40, No. 3, 1973, p.741
  17. G. J. Simitses, An Introduction to the Elastic Stability of Structures, Prentice-Hall, 1976
  18. A. P. S. Selvadurai, Elastic Analysis of Soil-Foundation Interaction, Elsevier, 1979
  19. W. F. Chen and E. M. Lui, Structural Stability-Theory and Implementation, Elsevier, 1987
  20. B. A. Abbas and J. Thomas, 'Dynamic Stability of Timoshenko Beams resting on an Elastic Foundation,' Journal of Sound and Vibration, Vol. 60, 1978, pp.33-44 https://doi.org/10.1016/0022-460X(78)90399-1
  21. R. H. Plaut and N. Olhoff, 'Optimal Forms of Shallow Arches with Respect to Vibration and Stability,' Journal of Structural Mechanics, Vol. 11, No. 1, 1983, pp.81-100