Stability of Columns Subject to Impulsive Loading

The stability criterion developed for simply supported columns determine a bound on the transverse motion of the column relative to the amplitude and duration of a prescribed force pulse and a set of initial perturbations. The conditions of stability are deduced from the characteristics of a class of Lyapunov functions constructed for this problem (Lyapunov's direct method). The stability of simply supported columns is presented for three specific example loadings: a constant thrust of infinite duration, a variable thrust of infinite duration, and a transient thrust of parabolic shape. The quality of the bounds is ascertained through comparison with the trajectory of the differential equation of motion, obtained by numerical integration.