Dynamic stability of a beam on an elastic foundation including stress wave effects

Abstract

This paper examines the dynamic stability of an elastic beam on the elastic foundation, in which the stress wave effect is taken into account. Based on Euler–Bernoulli beam theory, the dynamic response of the elastic beam on the elastic foundation to a small transverse perturbation is analyzed. By considering the stress wave propagation in the beam and the constraint of the elastic foundation, the critical bifurcation condition of elastic beam is derived, and the critical axial load of the elastic beam is predicted. Furthermore, the effects of the elastic foundation and the beam length on buckling condition are discussed by using numeric examples. Finally, an approximate solution of critical axial load for elastic beam on the elastic foundation is provided, which may be used to investigate elastic beam buckling problem.