Effects of Longitudinal Inertia Upon the Parametric Response of Elastic Columns

Abstract

Analytical and experimental investigations have been performed in a study of longitudinal inertia effects upon the parametric response of a column under an axial load P(t) = P0 + P1 cos γt. The analysis has led to stability criteria, imposed on the load and longitudinal inertia parameters, which have shown good agreement with experimental results. A certain degree of scatter between experimental runs has been observed, though agreement within (italics) each run has been very good. The scatter, attributed to small misalignments and departure from axiality of loading, stems from the realignment procedure necessary between each experimental run. To facilitate prediction of parametric response, the analytical stability criteria have been plotted in the form of two bounding surfaces of an instability region in a three-dimensional parameter space. Use of this region permits description of the conditions and responses associated with parametric instability, and allows evaluation of the effects of disturbances.