Finite element dynamic analysis of beams on nonlinear foundations under uniform moving loads and vehicles
by Prof. Fernando Simões (Instituto Superior Técnico)
at Bât. L de Vinci - INSA-Lyon ( RAPP )
The vibration of beams on foundations subjected to moving loads is an important engineering problem, specifically in high-speed railway track and infrastructure design. It is well know that constant loads moving with a constant velocity on uniform beams supported by uniform foundations may lead to significantly different dynamic behavior, depending on the velocity magnitude; for some velocity ranges the oscillation amplitudes may become very large, thus endangering the structural and passengers safety.
This presentation is dedicated to the computation by the finite element method of the critical velocities of loads or vehicles moving on Euler-Bernoulli beams supported by uniform linear or nonlinear viscoelastic foundations of the Winkler type. Two types of physical nonlinearity of the foundation are considered: either a cubic law or a bilateral law differentiating between compression and tension. The finite element formulation of the problem is derived and the corresponding mass, damping and stiffness matrices are consistently obtained. The semi-discrete system of the governing dynamic equations is solved by the HHT-alpha method.