Mathematical Problems in Engineering
Volume 2010 (2010), Article ID 591786, 17 pages
doi:10.1155/2010/591786
Research Article
A Semianalytical Method for Nonlinear Vibration of Euler-Bernoulli Beams with General Boundary Conditions
1School of Industrial Manufacturing, Chengdu University, Sichuan 610106, China
2Department of Physics and Electronic Information, China West Normal University, Nanchong, Sichuan 637002, China
3School of Aerospace, Mechanical and Manufacturing Engineering, RMIT University, P.O. Box 71, Bundoora, Victoria 3083, Australia
Received 31 December 2009; Revised 17 April 2010; Accepted 3 June 2010
Academic Editor: Carlo Cattani
Copyright © 2010 Jian-She Peng 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
This paper presents a new semianalytical approach for geometrically nonlinear vibration analysis of Euler-Bernoulli beams with different boundary conditions. The method makes use of Linstedt-Poincaré perturbation technique to transform the nonlinear governing equations into a linear differential equation system, whose solutions are then sought through the use of differential quadrature approximation in space domain and an analytical series expansion in time domain. Validation of the present method is conducted in numerical examples through direct comparisons with existing solutions, showing that the proposed semianalytical method has excellent convergence and can give very accurate results at a long time interval.