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