Free vibration and buckling of heavy column with regular polygon cross-section

This paper deals with the free vibration and buckling of heavy column, considering its own self-weight. The column has a regular polygonal cross-section with a constant area. The column is applied to an external axial load as well as the self-weight. The five end conditions of the column are considered. Based on equilibrium equations of the column element, differential equations governing the vibrational and buckled mode shapes of column are derived. In solution methods, differential equations are numerically integrated by the direct integration method and eigenvalues of the natural frequency, buckling load and self-weight buckling length are calculated by the determinant search method. The numerical results of this study were in good agreement with those of the reference. Parametric study of the end condition, side number and self-weight on the natural frequency and buckling load was carried out.

Automated summary

This study investigated the free vibration and buckling of a heavy column considering its self-weight, deriving differential equations for vibrational and buckled mode shapes. Numerical integration and determinant search methods were used to calculate the natural frequency, buckling load, and self-weight buckling length. The parametric study of end conditions, side number, and self-weight on natural frequency and buckling load were conducted, showing good agreement with reference values.