FINITE ELEMENT MODELLING OF INFINITE EULER BEAMS ON KELVIN FOUNDATIONS EXPOSED TO MOVING LOADS IN CONVECTED CO-ORDINATES

The paper deals with the finite element method (FEM) solution of the problem with loads moving uniformly along an infinite Euler beam supported by a linear elastic Kelvin foundation with linear viscous damping. Initially, the problem is formulated in a moving co-ordinate system following the load using a Galilean co-ordinate transformation and subsequently the analytical solution to the homogeneous beam problem is shown. To be used in more complicated cases where no analytical solutions can be found, a numerical approach of the same problem is then suggested based on the FEM. Absorbing boundary conditions to be applied at the ends of the modelled part of the infinite beam are derived. The quality of the numerical results for single-frequency, harmonic excitation is tested by comparison with the indicated analytical solution. Finally, the robustness of the boundary condition is tested for a Ricker pulse excitation in the time domain.