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Chinese Journal of Mathematics - Volume 2014 2014, Article ID 565826, 13 pages -

Research ArticleDepartment of Mathematical Sciences, Federal University of Technology, Akure, Ondo State 340271, Nigeria

Received 3 December 2013; Accepted 23 January 2014; Published 23 March 2014

Academic Editors: B. Sun and J. Sun

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.


This paper investigates the flexural vibration of a finite nonuniform Rayleigh beam resting on an elastic foundation and under travelling distributed loads. For the solution of this problem, in the first instance, the generalized Galerkin method was used. The resulting Galerkin’s equations were then simplified using the modified asymptotic method of Struble. The simplified second-order ordinary differential equation was then solved using the method of integral transformation. The closed form solution obtained was analyzed and results show that, an increase in the values of foundation moduli and rotatory inertia correction factor reduces the response amplitudes of both the clamped-clamped nonuniform Rayleigh beam and the clamped-free nonuniform Rayleigh beam. Also for the same natural frequency, the critical speed for the moving distributed mass problem is smaller than that for the moving distributed force problem. Hence resonance is reached earlier in the former. Furthermore, resonance conditions for the dynamical system are attained significantly by both and for the illustrative end conditions considered.

Autor: Emem Ayankop Andi and Sunday Tunbosun Oni

Fuente: https://www.hindawi.com/


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