Keywords: multi-objective optimization, robustness, condensation, metamodels, viscoelastic damping, structural dynamics.

In the context of sound and passive vibration control of mechanical systems, the use of viscoelastic materials has been regarded as a convenient strategy in many types of industrial applications where the materials can be applied either as discrete or surface devices (free or constrained layer treatments). To enable efficient analysis and design of viscoelastic dampers as applied to real-world complex structures such as automobiles, airplanes, communication satellites, tall buildings and space structures to reduce the vibration levels, the multi-objective optimization approach is an important step in the design phases (pre-project and/or project steps) of the damped system. Unfortunately, the large number of cost function evaluations employed in optimization (reanalysis procedure) and the complexity of the finite element models for the industrial applications (large number of degrees of freedom), results in long and sometimes prohibitive calculation costs (computational effort) to obtain the optimal solutions. Moreover, the non-linear modelling behavior particularly involved for the typical dependency of the viscoelastic properties (storage and loss moduli) with respect to operational and environmental parameters (mainly temperature and vibration frequency), is observed [1]. To circumvent this drawback, one strategy proposed in this work is the use of multi-objective evolutionary algorithms (MOEAs) [2] combining robust condensation approach [3,4], and meta-models based on the neural networks [5].

The use of model reduction techniques is justified in an attempt to reduce the time cost evaluations in the optimization process. However, the principal difficulty in using such approach for the viscoelastically damped systems is in obtaining simultaneously a drastic reduction and a predictive model while preserving its capability to represent the dynamic behaviour of the damped system due to the structural modifications and the non-linear viscoelastic effects in the updating optimization process.

So, in this paper is an adaptation approach is aproposed of [4], based on the extension of the standard Ritz basis by the contribution of optimal residual static vectors. This robust basis is constructed in a way that takes into account the physical modifications and viscoelastic effects, in the lower frequency domain. This approach enabled us to avoid the updating of the exact analysis leading to a signficative time-reduction cost in the the design process.

Due to the non-linear viscoelastically behavior, the multi-layer perceptron (MLP) combining the back propagation algorithm is employed as approximation functions in order to reduce the time of the optimization evaluation. The present paper discusses some of the crucial issues of the modelling of viscoellastically damped systems and the use of MOEAs combining robust condensation and MLP, which is organized as follows: introductory comments are first presented regarding some aspects related with the use of the so called complex modulus model, with emphasis placed on its incorporation into the finite element matrices of the three layer sandwich beams and plates. Next, some comments are made concerning the non dominated sorting genetic algorithm (NSGA) incorporating the MLP as an approximation technique of the response of the viscoelastically damped system.

In this work, only the frequency response functions of the two-dimensional civil engineering structures such as trusses, and stiffened panel incorporating discrete and surface damping treatments, respectively, were analysed. In the numerical applications, the main interests were the optimization of the geometrical parameters, the optimal positions of the treatments and the temperature of the viscoelastic material for a number of damped modes, with the aim of augmenting the damped performance of the treatments. The numerical results, demonstrate the ability of the NSGA-MLP optimization approach for large viscoelastic damped systems to represent accurately such approximation functions and thus considerably reducing the computing time.

1

De Lima A.M.G., Stoppa M.H., Rade D.A. and Steffen V.J., "Sensitivity Analysis of Viscoelastic Structures", Proceedings of Xl International Symposium on Dynamic Problems of Mechanics, Ouro Preto-MG, 2005, Brazil.

2

Ait Brik B., Méthodologies de Conception Robuste et d'Optimisation dans un Contexte de Conception d'Architectures Mécaniques Nouvelles en Avant Projet, Thèse de doctorat, Université de Franche-Comté, 2005, France.

3

Balmès E. and Germès S., "Design Strategies for Viscoelastic Damping Treatment Applied to Automotive Components", International Modal Analysis Conference (IMAC), 2004.

4

Masson, G., Bouhaddi, N., Cogan, S., Laurant, L., "Component Mode Synthesis Method Adapted to Optimization of Structural Dynamic Behevior", Proceedings of International Modal Analysis Conference, XXI IMAC, Kissimmee, February, 3-6, 2003.

5

Soteris K.A., "Optimization of Solar Systems using Artificial Neural Networks and Genetic Algorithms", Applied Energy pp. 383-405, 2004.

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