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Shock and Vibration
Volume 17 (2010), Issue 4-5, Pages 507-520

Robust Optimal Design of a Nonlinear Dynamic Vibration Absorber Combining Sensitivity Analysis

R.A. Borges,1 A.M.G. de Lima,2 and V. Steffen Jr.3

1Federal University of Tocantins, Mathematic Department Campus Arraias, Av. Universitária, Centro, CEP 77330-000, Arraias-TO, Brazil
2Federal University of Itajubá, Mechanical Engineering Institute Campus José Rodrigues Seabra, P.O.Box 50, CEP 37500-903, Itajubá-MG, Brazil
3Federal University of Uberlândia, School of Mechanical Engineering Campus Santa Mônica, P.O.Box 593, CEP 38400-902, Uberlândia-MG, Brazil

Received 18 June 2010; Accepted 18 June 2010

Copyright © 2010 Hindawi Publishing Corporation. 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.


Dynamic vibration absorbers are discrete devices developed in the beginning of the last century used to attenuate the vibrations of different engineering structures. They have been used in several engineering applications, such as ships, power lines, aeronautic structures, civil engineering constructions subjected to seismic induced excitations, compressor systems, etc. However, in the context of nonlinear dynamics, few works have been proposed regarding the robust optimal design of nonlinear dynamic vibration absorbers. In this paper, a robust optimization strategy combined with sensitivity analysis of systems incorporating nonlinear dynamic vibration absorbers is proposed. Although sensitivity analysis is a well known numerical technique, the main contribution intended for this study is its extension to nonlinear systems. Due to the numerical procedure used to solve the nonlinear equations, the sensitivities addressed herein are computed from the first-order finite-difference approximations. With the aim of increasing the efficiency of the nonlinear dynamic absorber into a frequency band of interest, and to augment the robustness of the optimal design, a robust optimization strategy combined with the previous sensitivities is addressed. After presenting the underlying theoretical foundations, the proposed robust design methodology is performed for a two degree-of-freedom system incorporating a nonlinear dynamic vibration absorber. Based on the obtained results, the usefulness of the proposed methodology is highlighted.