한국구조물진단유지관리공학회 논문집 (Journal of the Korea institute for structural maintenance and inspection)

한국구조물진단유지관리공학회 (Korea Institute for Structural Maintenance Inspection)
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두 변수 탄성지반으로 지지된 원호형 등단면 띠기초의 자유진동

Free Vibrations of Circular Uniform Strips Resting on Two Parameter Elastic Foundation

  • 이종천 (원광대학교 토목환경도시공학부)
  • 투고 : 2008.08.09
  • 심사 : 2008.10.17
  • 발행 : 2009.01.30
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초록

이 논문은 직시각형 단면을 갖는 원호형 등단면 띠기초의 자유진동에 관한 연구이다. 띠기초를 지지하는 지반을 두 변수 탄성지반으로 모형화하였다. 두 변수 탄성지반으로 지지된 원호형 띠기초의 휨-비틀림 자유 진동을 지배하는 미분방정식을 유도하고 이를 수치해석하여 고유진동수 및 진동형을 산정하였다. 띠기초의 경계조건은 자유-자유로 하여 최저저차 4개의 고유진동수를 산정하였다. 수치해석의 결과로, 중심각, 깊이비, 접촉비, 탄성계수비, 지반변수 등 5개의 변수가 고유진동수에 미치는 영향을 보고하였다. 변위 및 합응력의 진동형을 그림으로 나타내었다. 실험을 통하여 이 연구의 결과를 검증하였다.

This paper deals with the free vibrations of circular strip foundations which have uniform solid rectangular cross-section. The ground which supports circular strips was modeled as the two parameter elastic foundation. Differential equations governing the flexural-torsional free vibrations of circular strips supported by such foundation were derived, and solved numerically for obtaining the natural frequencies and mode shapes. Boundary condition of free-free ends was considered for numerical examples. Four lowest natural frequencies according to the variations of five system parameters i.e. subtended angle, depth ratio, contact ratio, elasticity ratio and soil parameter are reported in the non-dimensional forms. Also, typical mode shapes of both deformations and stress resultants are presented in the figures. Experiment was conducted for validating the theory developed in this study.

키워드

참고문헌

  1. 이병구, 이용수, 오숙경, 이태은, "비균질 Pasternak 지반으로 지지된 집중질량을 갖고 면내력을 받는 후판의 자유진동", 대한토목학회 논문집, 제24권, 제1A호, 2004, pp.79-85
  2. Al-Khafaji, A.W. and Tooley, J.R. "Numerical Method in Engineering Practice", Reinhardt and Winston, USA, 1986
  3. De Rosa, M.A. and Maurizi, M.J., "The Influence of Concentrated Masses and Pasternak Soil on the Free Vibrations of Euler Beams-Exact Solution", Journal of Sound and Vibration, Vol. 212, 1988, pp. 573-581 https://doi.org/10.1006/jsvi.1997.1424
  4. Ewins, D.J., "Modal Testing : Theory and Practice", John Wiley & Sons, Inc., 1985
  5. Kok, A., "Dynamic Analysis of Beams on a Pasternak Foundation", Proceedings of the Fourth Conference on Computer in Civil Engineering, ASCE, 1986, pp. 553-560
  6. Lee, B.K., Oh, S.J. and K.K. Park., "Free Vibrations of Shear Deformable Circular Curved Beams Resting on Elastic Foundations", International Journal of Structural Stability and Dynamics, Vol. 2, No. 1, 2002, pp. 77-97pp https://doi.org/10.1142/S0219455402000440
  7. Paliwal, D.N., Sindhi, S.N. and Ahmad, A., "Hyper Shell on Pasternak Foundation", Journal of Engineering Mechanics, ASCE, Vol.118, No.5, 1992, pp. 1303-1316 https://doi.org/10.1061/(ASCE)0733-9399(1992)118:7(1303)
  8. Rashed, Y.F., Aliabadi, M.H. and Brebbia, C.A., "Formulation of Mindlin-Engesser Model for Stiffened Plate Vibration", Computer Method in Applied Mechanics and Engineering, Vol. 120, 1999, pp. 339-353 https://doi.org/10.1016/0045-7825(94)00064-T
  9. Shastry, B.P. and Rao, G.V., "Dynamic Stability of Cantilever Columns Resting on an Elastic Foundation", Computers & Structures, Vol.25, 1987, pp. 157-158 https://doi.org/10.1016/0045-7949(87)90227-6
  10. Selvadurai, A.P.S., "Elastic Analysis of Soil-Foundation Interaction", Elsevier, UK., 1979
  11. Timoshenko, S.P., "On the Correction for Shear of the Differential Equation for Transverse Vibrations of Prismatic Bars", Philosophical Magazine, Vol. 41, pp. 744-746 https://doi.org/10.1080/14786442108636264
  12. Volterra, E. and Gains, J.H., "Advanced Strength of Materials", Prentice-Hall, USA
  13. Wang, T.M. and Stephens, J.E., "Natural Frequencies of Timoshenko Beams on Pasternak Foundation, Journal of Sound and Vibration", Vol. 51, 1977, pp. 149-155 https://doi.org/10.1016/S0022-460X(77)80029-1
  14. Yokoyama, T., "Vibration Analysis of Timoshenko Beam-Column on Two-Parameter Elastic Foundations", Computers & Structures, Vol. 61, 1996, pp. 995-1007 https://doi.org/10.1016/0045-7949(96)00107-1