Dynamic Instability Analysis of Axially Compressed Castellated Columns

This paper presents an analytical study on the dynamic instability of castellated columns subjected to axial excitation loading. By assuming the instability modes, the kinetic energy and strain energy of the columns and the loss of the potential of the axially applied load are evaluated, from which the mass matrix, stiffness matrix, and geometric stiffness matrix of the system are derived. These matrices are then used for deriving dynamic equations and carrying out the analysis of dynamic instability of castellated columns by using Bolotin's method. The analytical expression for determining the critical excitation frequency of the columns is derived, which takes account for not only the shear influence of web openings but also the rotary inertia effect on the transverse vibration of the columns. Numerical examples are also provided for illustrating the dynamic instability behaviour of castellated columns when subjected to axial excitation loading. The results show that the consideration of the shear effect in castellated columns results in a shaft of the dynamic instability zone to low frequency side and a reduction of the width of the dynamic instability zone. The shear effect on the dynamic instability zone becomes more significant in the short column than in the long column, and in the wide flange column than in the narrow flange column.