Page:Influence of a Moving Mass on the Dynamic Behaviour of Viscoelastically Connected Prismatic Double-Rayleigh Beam System Having Arbitrary End Supports.pdf/1

 Hindawi Chinese Journal of Mathematics Volume 2017, Article ID 6058035, 30 pages https://doi.org/10.1155/2017/6058035

Jacob Abiodun Gbadeyan and Fatai Akangbe Hammed

Correspondence should be addressed to Jacob Abiodun Gbadeyan; j.agbadeyan@undefinedyahoo.com

Received 30 August 2016; Accepted 28 November 2016; Published 26 February 2017

Academic Editor: Maria Bruzón

Copyright © 2017 Jacob Abiodun Gbadeyan and Fatai Akangbe Hammed. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

This paper deals with the lateral vibration of a finite double-Rayleigh beam system having arbitrary classical end conditions and traversed by a concentrated moving mass. The system is made up of two identical parallel uniform Rayleigh beams which are continuously joined together by a viscoelastic Winkler type layer. Of particular interest, however, is the effect of the mass of the moving load on the dynamic response of the system. To this end, a solution technique based on the generalized finite integral transform, modified Struble's method, and differential transform method (DTM) is developed. Numerical examples are given for the purpose of demonstrating the simplicity and efficiency of the technique. The dynamic responses of the system are presented graphically and found to be in good agreement with those previously obtained in the literature for the case of a moving force. The conditions under which the system reaches a state of resonance and the corresponding critical speeds were established. The effects of variations of the ratio (𝛾1 ) of the mass of the moving load to the mass of the beam on the dynamic response are presented. The effects of other parameters on the dynamic response of the system are also examined.

1. Introduction

The problem of determining the dynamic response of elastic structures traversed by moving loads is of significant technological importance and various researchers (Engineers, Physicists, and Applied Mathematicians) continue to pay considerable attention to studying the various corresponding mathematical models [1–14]. Most of these studies have been carried out for simpler structures such as beams, plates, frames, and shells since such elastic structures form the fundamental components of various modern complex structures and the mathematical analysis involved is relatively less complicated. For instance, the trolleys of overhead travelling cranes which move on their girders, as well as bridges on which trains or vehicles move, may be modeled as moving loads on beam [5]. The theory of vibration of single-beam or single-plate system subjected to moving loads with different boundary conditions has been extensively developed with hundreds of articles on it [1–14]. Frýba [2], in particular, gave a comprehensive survey of some of the techniques for solving various versions of this problem. Some engineering applications of the theory of vibration of a single-beam or single-plate system carrying a moving load include the study of the dynamic behaviour of guided circular saws usually used in the wood products industry, modern high-speed precision machinery processes, design of railway bridges, and the machining processes [14]. However, there exist many problems of notable practical significance in many branches of modern industrial, mechanical, aerospace, and civil engineering for which the theory of vibration of single-beam system under a moving load may not hold and hence one has to resort to the vibration theory of double-beam, triple-beam, or multibeam systems traversed by a moving load. Examples of such problems include the vibration of composite materials which is usually modeled using double-beam system. Elastically connected concentric beams are also being used