Abstract
This chapter focuses on the dynamic stability of a column under random loading. It reviews the dynamic stability of a pin-ended column under certain types of random axial loading. It discusses the derivation of the Gaussian White Noise Load Variation. When the axial load variation p(t) has a reasonably flat spectrum in a wide neighborhood of the natural frequency of transverse vibration ω0 of the column, the analysis can be simplified by assuming p(t) to have a white spectrum. The chapter explores the stability of the column when the axial load variation p(t) is a Gaussian process but with a non-white spectrum. It discusses sufficient conditions for almost certain asymptotic stability under the assumption that p(t) is absolutely integrable, with probability one, in every finite time interval, and that the expectation of the absolute value |p(t)|is bounded.
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