Moving Mesh Modelling in the Frequency Domain for Induced Vibration Estimation of Vehicles on Beams Supported on Elastic Media

Abstract

Moving one-dimensional Bernoulli beam elements in the frequency domain are presented in this paper for applications on induced vibrations due to moving loads or vehicles in contact with rails or roads supported by elastic homogeneous media. The model can be used for dynamic response estimation of trains on railroad tracks or vehicles on roads. A conventional motionless finite-element strategy requires very large meshes to allow the estimation of induced vibration of a moving vehicle, because a large portion of the mesh is required to model the distance travelled by the vehicle during simulation, in addition to domains at both sides of the model to develop adequate boundary conditions. An alternative approach is the use of a moving mesh so that the vehicle does not approach the boundaries of the model; this determines a significant reduction of the mesh size. The moving mesh moves at the speed of the vehicle, maintaining the contact-points at fixed locations in the moving reference frame. This approach leads to a time-invariant model for constant velocity vehicle or moving load in the case of a homogeneous foundation. In this paper, the moving beam and foundation model is developed in the frequency domain, computing the dynamic stiffness matrix of moving beam elements on a visco-elastic foundation. In addition, random process modelling of roughness of the rails or road allows the assessment of its effect on induced vibration of moving vehicles on infinite media. Different vehicle models can be connected the moving mesh model, including different number of wheel axes by defining nodes of the mesh bellow each wheel, making the formulation very practical. Some application examples of the proposed modelling technique are presented and limitations of the technique are mentioned.