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Mathematical Problems in Engineering
Volume 2013, Article ID 737502, 12 pages
http://dx.doi.org/10.1155/2013/737502
Research Article

Application of Three Bioinspired Optimization Methods for the Design of a Nonlinear Mechanical System

1Department of Mathematics, Federal University of Goiás, Avendia Dr. Lamartine Pinto de Avelar 1120, 75704-220 Catalão, GO, Brazil
2School of Chemical Engineering, Federal University of Uberlândia, Avendia João Naves de Ávila 2121, Campus Santa Mônica, P.O. Box 593, 38408-144 Uberlândia, MG, Brazil
3School of Mechanical Engineering, Federal University of Uberlândia, Avendia João Naves de Ávila 2121, Campus Santa Mônica, P.O. Box 593, 38408-144 Uberlândia, MG, Brazil

Received 21 January 2013; Revised 9 June 2013; Accepted 10 June 2013

Academic Editor: Chong Wu

Copyright © 2013 Romes Antonio Borges 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

The present work focuses on the optimal design of nonlinear mechanical systems by using heuristic optimization methods. In this context, the nonlinear optimization problem is devoted to a two-degree-of-freedom nonlinear damped system, constituted of a primary mass attached to the ground by a linear spring and a secondary mass attached to the primary system by a nonlinear spring. This arrangement forms a nonlinear dynamic vibration absorber (nDVA), which is used in this contribution as a representative example of a nonlinear mechanical system. The sensitivity analysis of the suppression bandwidth, namely, the frequency range over which the ratio of the main mass displacement amplitude to the amplitude of the forcing function is less than unity, with respect to the design variables that characterize the nonlinear system based on the first order finite differences is presented. For illustration purposes the optimization problem is written as to maximize the suppression bandwidth by using three recent bioinspired optimization methods: Bees Colony Algorithm, Firefly Colony Algorithm, and Fish Swarm Algorithm. The results are compared with other evolutionary strategies.