Dynamic analysis of prestressed Bernoulli beams resting on two-parameter foundation under moving harmonic load

Abstract

This paper describes the dynamic analysis of prestressed Bernoulli beams resting on a two-parameter elastic foundation under a moving harmonic load by the finite element method. Using the cubic Hermitian polynomials as interpolation functions for the deflection, the stiffness of the Bernoulli beam element augmented by that of the foundation support and prestress is formulated. The nodal load vector is derived using the polynomials with the abscissa measured from the left-hand node of the current loading element to the position of the moving load. Using the formulated element, the dynamic response of the beams is computed with the aid of the direct integration Newmark method. The effects of the foundation support, prestress as well as excitation frequency, velocity and acceleration on the dynamic characteristics of the beams are investigated in detail and highlighted.