Vibration and stability of a beam with elastic supports and concentrated masses under conservative and nonconservative forces

A coherent algorithm for the exact determination of the free vibration frequency of beam systems and the establishing of their critical load levels under both static conservative and non-conservative loads is presented. The proposed algorithm is based on exact solutions for segments distinguished in beams, which when boundary conditions and continuity conditions are taken into account allow one to construct digitally a map of the variation in the frequency of the beams' vibration. The effectiveness of the proposed approach is demonstrated using examples mainly from the domain of the analysis of the stability of nonconservatively loaded beam systems. (C) 1998 Elsevier Science Ltd. All rights reserved.