Stability analysis of a damped polygenic systems with relocatable mass along its length

Abstract

The stability of a clamped-free rod subjected to a compressive follower force at its tip, and bearing one or two relocatable mass points, is investigated. The outcomes of the calculations either using Euler's beam theory and neglecting damping and rotary inertia or using Rayleigh's beam theory including damping and rotary inertia are compared with each other: An optimal location exists for the mass points in both cases, however, the optimum is less pronounced with Rayleigh's theory including damping and rotary inertia than with Euler's theory neglecting damping and rotary inertia. Hence, one may conclude that for a safe design damping and rotary inertia, of the beam's mass elements as well as of the masspoints, has to be taken into account. The results obtained are of interest in connection with aircraft wings carrying jet engines, with turbine blades having varying cross-sections, etc.