Transverse Motions of Bernoulli-euler Beam Resting on Elastic Foundation and under Two Concentrated Moving Loads

Abstract

Aims/Objectives: The aim is to obtain a closed form solutions of single-dimensional structural element of continuously supported by an elastic foundation. Thereafter, we classify the effects of the space d connecting the loads on the relevant partial differential equations governing the motion of the structural members. The study also analysis circumstances under which resonance occur in the dynamical systems involving structural members. Study Design: The single-dimensional structural element is a partial differential equation of order fourth order place on elastic Winkler foundation. The Bernoulli-Euler beam traversed by two moving loads. Place and Duration of Study: Department of Mathematical Sciences, Adekunle Ajasin University P.M.B. 01, Akungba-Akoko, Nigeria, between May 2019 and September 2019. Methodology: The principal equation of the single -dimensional beam model is governing by partial differential equation of the order four. For the single -dimensional beam problem, the solution techniques are based on the Fourier sine transformation. The governing partial differential equation of the order four was reduced to sequence of second order ordinary differential equations.