Journal of KSNVE (소음진동)

The Korean Society for Noise and Vibration Engineering (한국소음진동공학회)
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Free Vibrations and Buckling Loads of Tapered Beam-Columns of Regular Polygon Cross-section with Constant Volume

일정체적의 정다각형 단면을 갖는 변단면 보-기둥의 자유진동 및 좌굴하중

  • Published : 1996.10.01
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Abstract

The differential equation governing both the free vibrations and buckling loads of tapered beam-columns of regular polygon cross-section with constant volume were derived and solved numerically. The parabolic and sinusoidl tapers were chosen as the variable depth of cross-section for the tapered beam-column. In numerical examples, the clamped-clamped, hinged-clamped and hinged-hinged end constraints were considered. The variations of frequency parameters and first buckling load parameters with the non-dimensional system parameters are reported in figures, and typical vibrating mode shapes are presented. Also, the configurations of strongest columns were determined.

이 논문에서는 일정체적의 정다각형 단면을 갖는 보-기둥의 자유진동 및 좌굴하중을 지배하는 비분방정식을 유도하고 이를 수치해석하였다. 정다각형 단면의 단면깊이 변화식으로는 포물선식과 정현식을 채택하였고, 고정-고정, 회전-고정 및 회전-회전의 단부조건에 대하여 고유진동수 및 좌굴하중을 산출하였다. 수치해석의 결과로 무차원 고유진동수와 무차원변들 사이의 관계 및 무차원 좌굴하중과 단면비 사이의 관계를 그림에 나타내었다. 또한, 최강기둥의 단면비와 좌국하중을 산출 하였다.

Keywords

References

  1. Elements of Structural Optimization R. T. Hartka;Z. Grudal;M.P. Kamat
  2. Q.App. Math. v.23 On the Optimal Disign of a Vibrating Beam F.I. Niordson
  3. Intl. J. Solids Struct. v.9 Optimal Beam Frequencies by the Finite Element Displacement Method M.P. Kamat;G. J. Simites
  4. Intl. J. Num. Meth. Eng. v.9 Effect of Shear Deformations and Rltary Inertia on Optimum Beam Frequencies M.P. Kamat;G.J. Simites
  5. Archiv. Rat. Mech. and Anal. v.5 The Shape of the Strongest Column J.V. Keller
  6. J. App. Mech. ASME v.29 Strongest Columns and Isoperimetric Inequakities for Eigenvalues I. Tadjbakhsh;J.B. Keller
  7. J. App. Mech.,ASME v.34 The Strongest Column-An Energy Approach J.E. Taylor
  8. J. Math. and Mech. v.16 no.5 The Tallest Column J.B. Keller;F.I. Niordson
  9. Imt. J. Solids Struct. v.20 Pptimal Structural Design under Multiple Eigenbalue Constraints E.F. Masur
  10. Espermental Mechanics v.11 Stability Experments on the Strongest Columns and Cirdular Arches J.F. Wolson;D.M. Holloway;S.B. Biggers
  11. Dynamics of Structures(2nd Edition) R.W. Clough;J. Penzien
  12. Applied Numerical Methods B. Carnahan;H.A. Luther;J.O. Wilkes
  13. Theory of Elastic Stability S.P. Timoshenko;J. M. Gere