Dynamic Response to Moving Distributed Masses of Pre-Stressed Uniform Rayleigh Beam Resting on Variable Elastic Pasternak Foundation

As Adeoye,To Awodola

doi:10.33805/2576.8484.106

Abstract

The dynamic response to moving distributed masses of pre-stressed uniform Rayleigh beam resting on variable elastic Pasternak foundation is examined. The equation governing this problem is a fourth order partial differential equation with variable and singular co-efficients. To solve this cumbersome equation, the method of Galerkin approach is adopted to reduce the governing differential equation to a sequence of coupled second order ordinary differential equation which is then simplified further with modified asymptotic method of Struble. The more simplified equation is solved using the Laplace transformation technique. The closed form solutions obtained are analyzed in order to show the conditions of resonance, and to show that resonance is attained earlier in moving mass system than in the moving force system. The results in plotted graphs show that as the axial force, the rotatory inertia, foundation modulus and shear modulus increase, the deflection of the elastically supported non-uniform Rayleigh beam decreases in each case. The transverse deflections of the beam on variable Pasternak elastic foundation are higher under the action of moving masses than those when only the force effects of the moving load are considered. This implies that resonance is reached faster in moving mass problem than in moving force problem.

Highlights

Transport structures such as railway or bridges are subjected to moving vehicles which vary in both space and time
The objective of this paper is to extend this research work to elastically supported uniform Rayleigh beam on variable elastic biparametric foundation
To illustrate the analysis presented in this work, the uniform Rayleigh beam is taken to be of length L = 12.192 m, the load velocity c = 8.128 m/s and modulus of elasticity

Summary

Introduction

Transport structures such as railway or bridges are subjected to moving vehicles (loads) which vary in both space and time. The branch of transport has experienced great advances, characterized by increasing high speed and weights of vehicles These structures on which the vehicles move have been subjected to vibration and dynamic stress more than ever before. Problems of this type are mathematically cumbersome when the inertial effect of the load is taken into consideration The challenges of these designs have attracted the interest of many researchers in the fields of applied mathematics, mechanical engineering, applied physics and railway engineering. Some of these researchers include Fryba [1], who studied the vibration of solids and structures under moving loads. Teodoru [6] in his work, analyzed beam on elastic foundation by using finite difference approach

Objectives

Discussion

Conclusion