Stability and dynamics of beams on winkler elastic foundations

Abstract

AbstractThe dynamical properties of a foundation beam on a Winkler soil have been recently discussed by using the power series method14 and the finite element method.15, 17 – 19 The first method can be applied only if the Winkler soil is linearly distributed along the whole span: on the contrary, the second method is more general, but it requires considerable computational efforts.In this paper a recently developed discretization method has been shown to be particularly well suited for dynamic analysis of foundation beams, in the presence of second order destabilizing effects. The procedure is based on the Hamilton principle, and the equation of motion is deduced from the corresponding Lagrange equations.According to the proposed method, the structure is reduced to a set of rigid bars, connected together by elastic cells. The convergence of the method is shown to be quite rapid, so that a small number of Lagrangian coordinates has to be introduced, and the resulting eigenvalue problem can be easily solved.Numerical comparisons are also performed with the available data of the literature, and the agreement is shown to be excellent. Two particularly unusual cases are illustrated, in order to emphasize the method's peculiarities.Finally, the influence of the axial forces on the fundamental vibration frequency is discussed, both for conservative and non‐conservative forces.