Dynamic stability of cracked columns; the stiffness reduction method

A new formulation for the dynamic stability of cracked columns is proposed. in this formulation,a differential equation governing the free vibration of a cracked column subjected to compressive axialforce is derived. the solution of the proposed equation needs only the end conditions for its solution(similar to that of intact beam columns). the equation is solved using the laplace transform. bothconservative and non-conservative forces are considered. the closed form solution is then used in thedynamic stability investigation of the cracked column with different boundary conditions. the accuracy,efficiency and robustness of the work are verified through numerical examples.