The Mode Synthesis Method for Structures Subject to a Moving Load : 1st Report, A Uniform Beam Subject to a Moving Load

Abstract

This paper is concerned with the dynamic responses for structures subject to a moving load. The dynamic responses of the structures are obtained using the mode synthesis method. The transverse vibration of a beam when a vehicle moves on a beam is treated as a model example. The vehicle is modelled by a linear system with 6 degrees of freedom. The physical coordinates expressing the equations of motion for the beam and the vehicle are transformed into the modal coordinates. Since the resultant equations of motion for the structure and the moving load are coupled with time-dependent coefficients, the time histories of deflections of the beam at the mid-point, and the relative deflections of the vehicle are calculated using the PC-12 method, which is one kind of numerical integration method. The obtained results are compared with the experimental results, and the effectiveness of the proposed method is verified.