Effects of initial curvature on the dynamic stability of a beam with tip mass subjected to axial pulsating loads

Abstract

The linearized equation of motion in matrix form of an Euler-Bernoulli inextensible beam with initial curvature and a tip mass subjected to axial pulsating loads is formulated based on Lagrangian approach and the assumed mode method. The effect of initial curvature is shown to be contained in the kinetic energy of the tip mass as well as the work done by the axial loads. Using Bolotin's method, the linearized equation of motion is converted to the standard form of an eigenvalue problem for computing the principal instability regions. The initial curvature of the beam is found to have no effect on the dynamic stability of the beam if there is no tip mass. The effects of various prescribed initial shapes of the beam, the tip mass, the frequency and magnitude of load perturbation on the stability behaviors are investigated for a simply supported beam.