Effect of Axial Resonance on the Dynamic Stability of Thin-Walled Columns


The dynamic stability of a thin-walled column of arbitrary open cross section subjected to a pulsating axial force is studied wherein the effect of longitudinal inertia has been included in the calculation of the internal axial stress. An eigenfunction-expansion technique yields a system of ordinary differential equations with periodic coefficients, the stability of which is then examined. The effect of longitudinal inertia was found to increase the width of the -³Mathieu-instability-³ regions, especially for those modes near the frequency of axial resonance. A numerical study showed that those modes with frequencies within 60% of the fundamental axial resonance had their unstable regions amplified by more than 10%. Combination resonances between various modes having the same or different mode numbers were also found when the effects of axial inertia were included and a multi-mode solution was sought. The effect of viscous damping is also briefly discussed.

Meeting Name

13th Midwest Mechanical Conference


Mechanical and Aerospace Engineering

Document Type

Article - Conference proceedings

Document Version


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© 1973 Elsevier, All rights reserved.

Publication Date

01 Jan 1973

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