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Civil-Comp Proceedings
ISSN 1759-3433
CCP: 88
Edited by: B.H.V. Topping and M. Papadrakakis
Paper 105

Topology Optimization Based on the Level-Set Method for Passive Damping of Structures

S. Bouzidi1, M.L. Bouazizi1, M. Guedri1 and N. Bouhaddi2

1Preparatory Engineering Institute of Nabeul (IPEIN), Tunisia
2FEMTO-ST Institute UMR 6174 - Applied Mechanics Laboratory R. Chaléat, Besançon, France

Full Bibliographic Reference for this paper
S. Bouzidi, M.L. Bouazizi, M. Guedri, N. Bouhaddi, "Topology Optimization Based on the Level-Set Method for Passive Damping of Structures", in B.H.V. Topping, M. Papadrakakis, (Editors), "Proceedings of the Ninth International Conference on Computational Structures Technology", Civil-Comp Press, Stirlingshire, UK, Paper 105, 2008. doi:10.4203/ccp.88.105
Keywords: vibration damping, piezoelectric structure, viscoelastic material, optimization, level-set method, finite element analysis.

In dynamic systems, special attention must be paid to the reduction of vibrations and the noise that accompanies these vibrations. The damping of the vibratory phenomena is a key factor in the performance improvement of many mechanical systems because it reduces the risk of fatigue of the components and noise reducing due to vibrations.

In the context of the passive damping of vibrations and noise, the use of the shunted piezoelectric materials (continuous dispositive) or viscoelastic treatments (continuous or discrete dispositive) becomes an interesting and effective means in several industrial applications. To reduce the costs and the added masses to the structure, it is more important and more effective to introduce the damping as shared patches on the treated structure.

The piezoelectric material generates an electric field in response to a mechanical deformation (used as a sensor) or inversely, a mechanical deformation in response to an electric field (used as an actuator). Several models were represented in the literature [1].

The use of viscoelastic materials has been regarded as a convenient strategy in many types of industrial applications, where these materials can be applied either as discrete devices, such as translational and/or rotational mounts, or surface treatments (free or constrained layers), at a relatively moderate cost of application and the maintenance as compared to other more involved strategies, such as active control [2].

The objective of our work is the damping of the first modes in a priori fixed band of a free plate by a method of semi-active damping using a layer of piezoelectric material with a shunted electric circuit. In another example of our work, we use a viscoelastic material to attenuate the resonance amplitudes of the frequency response functions corresponding to the GARTEUR airplane model. For that, it is necessary to place damping at several places in the structure. Furthermore, for a gain in the mass, the cost of the procedure, and to avoid the big frequency gap of the structure, one can resort to shape optimization. The strategy of the shape optimization is based on the level-set method.

In this study, a methodology of optimal shape design of these piezoelectric and viscoelastic damping absorbers dedicated to the complex structures is proposed. This exploits on the one hand, a method of optimization of shape and topology, based on the level-set strategy [3] and on the other hand it exploits the use of finite elements models.

Crawley E.F., deLuis J., "Use of piezoelectric actuators as elements of intelligent structures", AIAA J., 25(10), 1373-1385, 1987. doi:10.2514/3.9792
Nashif A.D., Jones D.I.G., Henderson J.P., "Vibration damping", John Wiley & Sons, New York, 1985.
Sethian J.A., Wiegmann A., "Structural Boundary Design via Level Set and Immersed Interface Methods", Journal of Computational Physics, 163, 489-528, 2000. doi:10.1006/jcph.2000.6581

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