Finite element dynamic analysis of beams on nonlinear elastic foundations under a moving oscillator

This paper presents a study on the dynamic response of beams on elastic foundations, subjected to a uniformly moving oscillator. Using a finite element model programmed within a MATLAB environment the response of the system is studied for three different types of mechanical behaviour of the foundation: (a) linear elastic (classical Winkler model), (b) nonlinear elastic (in which the foundation reaction displays a cubic dependence on the beam displacement) and (c) bilinear elastic (with different compressive and tensile stiffnesses). The effects of the oscillator's natural frequency and velocity and of the foundation's stiffness and damping are investigated. In particular, critical velocities of the oscillator and ranges of velocities for which the system is dynamically unstable are numerically determined for the first time in the above mentioned nonlinear cases.