Study of Second Regions of Dynamic Instability of a Uniform Beam

Abstract

Dynamic instability of a beam is solved for second regions of instability. The governing equations are of the Mathieu—Hill type, where the parametric regions are sought. While the solution to the first region of a beam has been widely reported, there is none available in the literature for the second region. In this work, the regions are determined by the finite element method. Bolotin determined the solution analytically, but it is more of a qualitative solution of the problem. In this work, a quantitative solution is sought from the finite element method. The width of the regions are significant. The effects of the static load factor and the dynamic load factor are obtained.