Dynamic behaviour of non-uniform Bernoulli-Euler beams subjected to concentrated loads travelling at varying velocities.

Abstract

This paper investigates the dynamics behaviour of non-uniform Bernoulli-Euler beams subjected to concentrated loads ravelling at variable velocities. The solution technique is based on the Generalized Galerkin Method and the use of the generating function of the Bessel function type. The results show that, for all the illustrative examples considered, for the same natural frequency, the critical speed for the system consisting of a non-uniform beam traversed by a force moving at a non-uniform velocity is greater than that of the corresponding moving mass problem. It was also found that, for fixed axial force, an increase in foundation moduli reduces the response amplitudes of the dynamical system. Furthermore, it was shown that the transverse-displacement amplitude of a clamped-clamped non-uniform Bernoulli-Euler beam traversed by a load moving at variable velocities is lower than that of the cantilever. The response amplitude of the same dynamical systems which is simply supported is higher than those which consist of clamped-clamped or clamped-free (Cantilever) end conditions. Finally, an increase in the values of foundation moduli and axial force reduces the critical speed for all variants of the boundary conditions

Journal of the Nigerian Association of Mathematical Physics Vol. 9 2005: pp. 79-102