Analytical Solution for the Boundary Value Problem of Elastic Beams Subjected to Distributed Load

Abstract

Analytical solution for the boundary value problem (BVP) of elastic beams subjected to distributed load was investigated. Based on the study, dynamic application curves are developed for beam deflection. The partial differential equation of order four were analysed to determine the dynamic response of the elastic beam under consideration and solved analytically. Effects of different parameters such as the mass of the load, the length of the moving load, the distance covered by the moving load, the speed of the moving and the axial force were considered. Result revealed that the values of the deflection with acceleration being considered are higher than the system where acceleration of the moving load is negligible. These obtained results are in agreement with the existing results.

Free Vibrational Analysis of Non-uniform Double Eulerbernoulli Beams on a Winkler Foundation Using Laplace Differential Transform Method

“…The accuracy of the proposed method was validated through numerical simulations, and the effect of the foundation stiffness and the non-uniformity of the beam on the natural frequencies was investigated. Usman et al (2021aUsman et al ( , 2021b solved the governing equation of the Euler-Bernoulli beam on Winkler support analytically. Ghannadiasl (2021) investigated the free vibration of tapered Euler-Bernoulli beams on Winkler foundations using the Quintic B-spline collocation method.…”