Dynamic Optimal Shapes of Simple Beam-Columns with Constant Volume

일정체적 단순지지 보-기둥의 동적 최적단면

  • Received : 1997.02.12
  • Published : 1997.06.30

Abstract

The main purpose of this paper is to determine the dynamic optimal shapes of simple beam-columns with the constant volume. The parabolic function is chosen as the variable equation for the depth of regular polygon cross-section. The ordinary differential equation including the effect of axial load is applied to calculate the natural frequencies. The Runge-Kutta and Regula-Falsi methods are used to integrate the differential equation and compute the frequencies, respectively. Then the dynamic optimal shape whose lowest natural frequency is highest is determined by reading the critical value of the frequency versus section ratio curve plotted by the frequency data. In the numerical examples, the simple beam-columns are analysed and the numerical results of this study are shown in tables and figures.

Acknowledgement

Grant : 연속보의 동적 최적설계에 관한 연구

Supported by : 한국학술진흥재단

References

  1. Int. J. Non-Linear Mechanics v.28 no.5 Elastica of Cantilevered Beams with Variable Cross Section Lee, B.K.;Wilson, J.F.;Oh, S.J.
  2. Applied Numerical Methods Carnahan, B.;Luther, H.A.;Wilkes, J.O.
  3. Journal of Korean Society of Noise and Vibration Engineering v.6 no.5 Free Vibrations and Buckling Loads of Tapered BeamColumns of Regular Polygon Cross-Section with Con- stant Volume Lee, B.K.;Mo, J.M.
  4. Dynamics of Structures Clough, R.W.;Penzien, J.
  5. Journal of Sound and Vibration v.138 no.1 Free Vibrations of Arches with Variable Curvature Lee, B.K.;Wilson, J.F.
  6. J. App. Mech., ASME v.29 Strongest Columns and lsoperimetric Inequalities for Eigenvalues Tadjbakhsh, I.;Keller, J.B.
  7. J. Math. and Mech. v.16 no.5 The Tallest Column Keller, J.B.;Niordson, F.I.
  8. J. Appl. Mech., ASME v.34 The Strongest Column-An Energy Approach Tayor, J.E.
  9. Experimental Mechanics v.11 Stability Experiments on the Strongest Columns and Circular Arches Wilson, J.F.;Holloway, D.M.;Biggers, S.B.
  10. Int. J. Solids Struct. v.20 Optimal Structural Desgin under Multiple Eigenvalue Constraints Masur, E.F.
  11. Intl. J. Num. Meth. Eng. v.9 Effect of Shear Deformations and Rotary Inertia on Optimum Beam Frequencies Kamat, M.P.;Simites, G.J.
  12. Archiv. Rat. Mech. and Anal. v.5 The Shape of the Strongest Column Keller, J.B.
  13. Elements of Structural Optimization Haftka, R.T.;Grudal, Z.;Kamat, M.P.
  14. Q. App. Math. v.23 On the Optimal Design of a Vibrating Beam Niordson, F.I.
  15. IntI. J. Solids Stuct v.9 Optimal Beam Frequencies by the Finite Element Displacement Method Kamat, M.P.;Simites, G.J.