Dynamic behavior of beam with an elastic foundation under the extended moving load for electromagnetic launch rail-structure

Abstract

The distributed load with loaded area being extended over the whole structure (i.e., the extended moving load) that occurs during the operation of an electromagnetic launch rail-structure, is different from loading cases studied previously such as the concentrated load or distributed load on a finite segment (i.e., the single moving load), or a series of single moving loads in a periodic pattern (i.e., the periodic moving load). In this paper, a nonlinear finite element model is proposed by modeling the rail-structure as a Euler-Bernoulli based beam on an elastic foundation to study the dynamics of rail-beam under such an extended moving load. The proposed model is firstly verified by comparison with the analytical solution for the rail-vibration response under the extended moving load at constant speed, and the model feasibility is further revealed by comparison with the experimental results of rail strain. The significant differences of rail vibration modes are observed between the extended moving load and the single, or periodic moving load. Moreover, the maximum error of the middle of the rail between the linear forcing and nonlinear forcing will decrease with the increase in the foundation elastic modulus, but increases with the increase in the pulse current. Those results will improve our understanding on dynamics of beam under the more comprehensive loading cases.