NONLINEAR DYNAMIC ANALYSIS OF FLEXIBLE BEAMS TRAVERSED BY A MOVING MASS

Abstract

This article deals with nonlinear dynamic analysis of flexible beams subjected to a moving mass load. The concept of fictitious loads to account for the kinematic corrections was applied to formulate the finite element model, which alleviates the needs to construct the nonlinear equations of motion and to perform the associated complicated solution process. The Timoshenko beam theory was considered to account for the shearing and rotary inertia effects. The nodal coordinates were iteratively updated until a specified convergence criterion was met for numerical analysis of the system dynamic response. The dynamic displacement responses were computed to illustrate the impact of the moving mass load. The effect of the mass ratio, defined as the ratio between the moving mass and the total mass of the support beam, on the impact of the structures was examined. This study shows that for the case of a larger mass ratio and a higher moving speed, the linear model can be in serious error and the nonlinear analysis is required for accurate analysis to ensure operation accuracy and safety. It can be seen from the analysis results that the dynamic impact of the moving mass load can be appreciably higher than that in the static condition. As opposed to the conventional understanding, the free response for the analysis case considered here can be significantly more severe than the forced response. The dynamic analysis for the case of a flexible beam traversed by an accelerated moving mass exhibits some interesting results on the effect of dynamic impact and care must be taken in designing a support structure to undergo this type of loading case.