investigation of the stability and vibration of cracked columns under compressive axial load

in this paper, a new analytical method is proposed to study the effect of crack and axial load on vibration behavior and stability of the cracked columns. using the local flexibility model, the crack has been simulated by a torsional spring with connecting two segments of column in crack location. by solving governing eigenvalue equation, the effect of crack parameters and axial load on the natural frequencies and buckling load as well as buckling load are investigated. the results show that the presents of crack cause to reduction in natural frequencies and buckling load whereas this reduction is affected by the location and depth of the crack. furthermore, the tensiel and compressive axial load increase and decrease the natural frequencies, respectively. in addition, as the compression load approaches to certain value, the fundamental natural frequency reaches zero and instability occurs. the accuracy of the model is validated through the experimental data reported in the literature.