Table of Contents
Journal of Computational Engineering
Volume 2014, Article ID 140407, 19 pages
http://dx.doi.org/10.1155/2014/140407
Research Article

Dynamic Analysis under Uniformly Distributed Moving Masses of Rectangular Plate with General Boundary Conditions

1Department of Mathematics, Nigerian Defence Academy, Kaduna State, Kaduna 800001, Nigeria
2Department of Mathematical Sciences, Federal University of Technology, Ondo State, Akure 340001, Nigeria

Received 3 December 2013; Revised 25 April 2014; Accepted 12 May 2014; Published 19 June 2014

Academic Editor: Nam-Il Kim

Copyright © 2014 Emem Ayankop Andi and Sunday Tunbosun Oni. 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.

Abstract

The problem of the flexural vibrations of a rectangular plate having arbitrary supports at both ends is investigated. The solution technique which is suitable for all variants of classical boundary conditions involves using the generalized two-dimensional integral transform to reduce the fourth order partial differential equation governing the vibration of the plate to a second order ordinary differential equation which is then treated with the modified asymptotic method of Struble. The closed form solutions are obtained and numerical analyses in plotted curves are presented. It is also deduced that for the same natural frequency, the critical speed for the system traversed by uniformly distributed moving forces at constant speed is greater than that of the uniformly distributed moving mass problem for both clamped-clamped and simple-clamped end conditions. Hence resonance is reached earlier in the uniformly distributed moving mass system. Furthermore, for both structural parameters considered, the response amplitude of the moving distributed mass system is higher than that of the moving distributed force system. Thus, it is established that the moving distributed force solution is not an upper bound for an accurate solution of the moving distributed mass problem.