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Shock and Vibration
Volume 16 (2009), Issue 5, Pages 455-466

Design Optimization for Vibration Reduction of Viscoelastic Damped Structures Using Genetic Algorithms

Zhengchao Xie, W. Steve Shepard Jr., and Keith A. Woodbury

The University of Alabama, Department of Mechanical Engineering, 290 Hardaway Hall, Box 870276, Tuscaloosa, AL 35487, USA

Received 15 May 2006; Revised 29 May 2008

Copyright © 2009 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.


Due to the large number of design variables that can be present in complex systems incorporating visco-elastic damping, this work examines the application of genetic algorithms in optimizing the response of these structures. To demonstrate the applicability of genetic algorithms (GAs), the approach is applied to a simple viscoelastically damped constrained-layer beam. To that end, a finite element model (FEM) derived by Zapfe, which was based on Rao's formulation, was used for a beam with constrained-layer damping. Then, a genetic algorithm is applied to simultaneously determine the thicknesses of the viscoelastic damping layer and the constraining layer that provide the best response. While the targeted response is ultimately at the discretion of the designer, a few different choices for the fitness function are shown along with their corresponding impact on the vibratory response. By integrating the FEM code within the GA routine, it is easier to include the frequency-dependence of both the shear modulus and the loss factors for the viscoelastic layer. Examples are provided to demonstrate the capabilities of the method. It is shown that while a multi-mode optimization target provides significant reductions, the response for that configuration is inferior to the response when only single-mode reduction is considered. The results also reveal that the optimum configuration has a lower response level than when a thick layer of damping material is used. By demonstrating the applicability of GA for a simple beam structure, the approach can be extended to more complex damped structures.