Exact Vibration Solution for initially stressed Beams resting on Elastic Foundation and subjected to partially distributed masses

Abstract

In this paper, the response to moving distributed masses of a simply supported elastic thick beam resting on an elastic foundation with exponential rigidity is presented. The technique is based on the generalized Galerkin’s method and integral transformation. Exact solutions are obtained and the convergence of these solutions established. Solutions obtained are calculated for various values of foundation moduli K, axial force N, and damping coefficient 0 . It is observed that, as the values of these structural parameters increase, the transverse deflections of the finite elastic beam under the actions of moving masses decreases. Furthermore, the conditions under which the vibrating systems will experience resonance phenomenon are highlighted. Results presented in this paper are useful in structural engineering design and could also form basis for further investigations in this area of study.