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Mathematical Problems in Engineering
Volume 2013 (2013), Article ID 148537, 12 pages
http://dx.doi.org/10.1155/2013/148537
Research Article

Approximations for Large Deflection of a Cantilever Beam under a Terminal Follower Force and Nonlinear Pendulum

1Electronic Instrumentation and Atmospheric Sciences School, University of Veracruz, Cto. Gonzalo Aguirre Beltrán S/N, 91000 Xalapa, VER, Mexico
2Department of Mathematics, Zhejiang University, Hangzhou 310027, China
3Micro and Nanotechnology Research Center, University of Veracruz, Calzada Ruiz Cortines 455, 94292 Boca del Rio, VER, Mexico
4National Institute for Astrophysics, Optics and Electronics, Luis Enrique Erro No. 1, Sta. María, 72840 Tonantzintla, PUE, Mexico
5Facultad de Ingenieria Civil, Universidad Veracruzana, Venustiano Carranza S/N, Col. Revolucion, C.P. 93390, Poza Rica, VER, Mexico

Received 13 November 2012; Accepted 16 January 2013

Academic Editor: Gerhard-Wilhelm Weber

Copyright © 2013 H. Vázquez-Leal et al. 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

In theoretical mechanics field, solution methods for nonlinear differential equations are very important because many problems are modelled using such equations. In particular, large deflection of a cantilever beam under a terminal follower force and nonlinear pendulum problem can be described by the same nonlinear differential equation. Therefore, in this work, we propose some approximate solutions for both problems using nonlinearities distribution homotopy perturbation method, homotopy perturbation method, and combinations with Laplace-Padé posttreatment. We will show the high accuracy of the proposed cantilever solutions, which are in good agreement with other reported solutions. Finally, for the pendulum case, the proposed approximation was useful to predict, accurately, the period for an angle up to yielding a relative error of 0.01222747.