Application of Volterra integral equations in the dynamics of a multi-span Rayleigh beam subjected to a moving load

Abstract

Abstract The dynamic behavior of a Rayleigh multi-span uniform continuous beam system that is traversed by a constant moving force or a uniformly distributed load is considered. The load is moving with a constant velocity. The problem is solved using an analogue of the static force method and, instead of an algebraic set of equations, a set of Volterra integral equations. The method presented in the work combines the analytical approach with the numerical procedure. The primary structure (primary beam) is a simply supported Rayleigh beam. In order to find the solution for multi-span continuous beams using sets of Volterra integral equations, the dynamic response of the finite, simply supported beam under a moving load and concentrated forces acting at a fixed place is first considered. Volterra's integral equations were formulated from the conditions that the displacements in the place of the supports, which are caused by the moving load and forces acting in the place of supports in the primary beam are equal to zero. Volterra's integral equations were solved numerically. Applications of the presented solutions in a stochastic dynamic multi-span Rayleigh beam are also presented.