Analytical Solution for the Boundary Value Problem of Euler-Bernoulli Beam Subjected to Accelerated Distributed Load

Mustapha Adewale Usman,Debora Oluwatobi Daniel,Fatai Akangbe Hammed

doi:10.21315/jes2021.17.1.2

Mustapha Adewale Usman, Debora Oluwatobi Daniel + Show 1 more

Open Access

https://doi.org/10.21315/jes2021.17.1.2

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Abstract

The study of dynamic response of beam-like structures to moving or static loads has attracted and still attracting a lot of attention due to its wide range of applications in the construction and transportation industry especially when transverse by travelling masses. Hence, analytical solution for the boundary value problem (BVP) of elastic beams subjected to distributed load was investigated. 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 increases than the system where acceleration of the moving load is negligible.

Highlights

Most physical and engineering boundary value problem (BVP) can be modelled as functional equations
Analytical solutions for BVPs are always preferable compared to numerical solutions as they are more general and give a better understanding of the model behaviour
Acceleration of a travelling mass over a structural system, highly affects the dynamic response of the structural system. This will give the engineers some advantages to make a more realistic modelling of structural systems under accelerating mass motion than the classical methods that omit the initial effects of accelerating mass

Summary

Introduction

Most physical and engineering boundary value problem (BVP) can be modelled as functional equations. Several analytical and numerical methods are being developed to obtain approximate solutions for such models.[1] Analytical solutions for BVPs are always preferable compared to numerical solutions as they are more general and give a better understanding of the model behaviour. Due to great practical importance for technical engineers, the analysis of the dynamic behaviour of beams on elastic foundations has attracted many researchers in the century and has been the object of study by a huge number of researchers until now. Many researchers have studied the dynamic structure of a distributed load subjected to various types of load.[2,3,4,5,6,7,8,9,10] They have formulated the problem using the analytical and numerical techniques since the pioneer studies of Winkler.[11]

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