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Shock and Vibration
Volume 13, Issue 4-5, Pages 545-558

Sensitivity Analysis of Viscoelastic Structures

A.M.G. de Lima,1 M.H. Stoppa,2 D.A. Rade,1 and V. Steffen Jr.1

1Federal University of Uberlândia, School of Mechanical Engineering, Brazil
2Federal University of Goiás, Department of Mathematics Campus Santa Mônica, P.O. Box 593, CEP 38400-902, Uberlândia, MG, Brazil

Received 19 July 2006; Revised 19 July 2006

Copyright © 2006 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.


In the context of control of sound and vibration of mechanical systems, the use of viscoelastic materials has been regarded as a convenient strategy in many types of industrial applications. Numerical models based on finite element discretization have been frequently used in the analysis and design of complex structural systems incorporating viscoelastic materials. Such models must account for the typical dependence of the viscoelastic characteristics on operational and environmental parameters, such as frequency and temperature. In many applications, including optimal design and model updating, sensitivity analysis based on numerical models is a very usefull tool. In this paper, the formulation of first-order sensitivity analysis of complex frequency response functions is developed for plates treated with passive constraining damping layers, considering geometrical characteristics, such as the thicknesses of the multi-layer components, as design variables. Also, the sensitivity of the frequency response functions with respect to temperature is introduced. As an example, response derivatives are calculated for a three-layer sandwich plate and the results obtained are compared with first-order finite-difference approximations.