Finite element dynamic analysis of finite beams on a bilinear foundation under a moving load

The present paper is concerned with the behaviour of finite elastic beams, acted by a moving transverse concentrated load, interacting with elastic foundations of different stiffnesses in compression and in tension. Using finite element analyses, the displacement amplitudes and the critical velocities of the load on a UIC-60 rail are computed and their dependence with respect to the difference between the foundation׳s moduli in compression and in tension is evaluated. The limit case of a tensionless foundation is as well analyzed. The numerical algorithm relies on the internal force vectors and tangent stiffness matrices computed exactly with automatic symbolic manipulation.