Dynamic stability of a beam on multiple supports subject to pulsating conservative axial loads

Abstract

The equation of motion of a beam on multiple supports, subject to prescribed time-dependent conservative axial loads, is formulated based on Hamilton's principle and the assumed mode method. The effects of sinusoidal perturbations in respect of the axial loads are then examined using Bolotin's method. The respective regions of instability are determined by converting the resulting equations of boundary frequencies into the standard form of a generalized eigenvalue problem. Instability regions are presented for various combinations of support configuration, average value and amplitude of the sinusoidal perturbations of the axial loads.