Abstract
The problem of dynamic stability of an elastic column with pinned ends subjected to non-stationary compressive axial loads is considered. The method of optimal Lyapunov functions for differential inclusions is applied to obtain sufficient conditions of stability of the column in the case of bounded loads. The obtained results, improving and generalising the classical solutions to the dynamic Euler problem, may be useful in designing civil engineering structures and mechanical systems consisting of compressed columns. The possibility of optimisation of the column characteristics with respect to its stability properties (e.g. stability margins in the space of parameters) is pointed out.Keywords:
elastic column, non-stationary loads, column stability, , Laypunov function, differential inclusionReferences
1. Z. OSIŃSKI, Theory of vibration [in Polish], PWN, Warszawa 1978.
2. B. SKALMIERSKI and A. TYLIKOWSKI, Stability of dynamical systems [in Polish], PWN, Warszawa 1973.
3. J.A. LEPORE and H.C. SHAH, Dynamic stability of axially loaded columns subjected to stochastic excitation, AIAA Journal, 6, 8, 1515–1521, 1968.
4. A. MUSZYŃSKA and B. RADZISZEWSKI, Exponential stability as a criterion of parametric modification in vibration control, Nonlinear Vibration Problems, 20, 175–191, PWN 1981.
5. A. OSSOWSKI, On the exponential stability of non-stationary dynamical systems, Nonlinear Vibration Problems, 21, 109–121, PWN 1989.
2. B. SKALMIERSKI and A. TYLIKOWSKI, Stability of dynamical systems [in Polish], PWN, Warszawa 1973.
3. J.A. LEPORE and H.C. SHAH, Dynamic stability of axially loaded columns subjected to stochastic excitation, AIAA Journal, 6, 8, 1515–1521, 1968.
4. A. MUSZYŃSKA and B. RADZISZEWSKI, Exponential stability as a criterion of parametric modification in vibration control, Nonlinear Vibration Problems, 20, 175–191, PWN 1981.
5. A. OSSOWSKI, On the exponential stability of non-stationary dynamical systems, Nonlinear Vibration Problems, 21, 109–121, PWN 1989.
