Stability and non-stationary vibration of columns under periodic loads

The procedure of digital simulation to investigate the dynamic problems of continuous systems with a periodically time-varying parameter is first stated. Then the procedure is applied to the instability problem of a cantilevered column subjected to an axial periodic load (Euler-type problem) and to the problem of the same column subjected to a tangential periodic load (Beck-type problem). The principal regions of dynamic instability for the two problems are determined, and the non-stationary vibrations near the stability-instability critical regions are investigated. The relations between Euler-type and Beck-type problems are also investigated by using an analogue simulation method.