Keywords: sandwich structures, passive damping, active damping, gradient optimisation, genetic algorithms, co-located control.

In this paper, recent developments in optimisation of hybrid active-passive damping treatments of sandwich structures are presented. In order to control the dynamic response of sandwich laminated structures with a viscoelastic core, laminated anisotropic constraining layers, and piezoelectric sensor and actuator face layers, a finite element model has been formulated using a mixed layerwise approach, by considering a higher order shear deformation theory (HSDT) to represent the displacement field of the viscoelastic core, and a first order shear deformation theory (FSDT) for the displacement fields of the adjacent face layers.

The layerwise model is a generalisation of the equivalent single layer presented by Araújo et al. [1], and is based on an eight nodded plate/shell finite element, with 17 mechanical degrees of freedom per node, after imposing inter-layer displacement continuity. Additionally, one electric potential degree of freedom is considered for each sensor and/or actuator layer, at the element level. The complex modulus approach is used for the viscoelastic material behaviour, and the dynamic problem is solved in the frequency domain, using viscoelastic frequency dependent material data for the core, resulting in a complex and frequency dependent stiffness matrix.

Optimisation of passive damping is conducted for the maximisation of modal loss factors, using as design variables the viscoelastic core thickness, as well as the constraining elastic face laminae thicknesses and fibre orientation angles. The optimisation problems are solved using gradient-based optimisation [2] and/or genetic algorithms [3] as appropriate. The model developed has been applied successfully for sandwich beams and plates and the optimal results are compared and discussed with an alternative optimisation model based on three-dimensional finite elements from the commercial package ABAQUS [4] and the implementation of a genetic algorithm.

Active damping maximisation is also conducted to find the optimal position of a predefined number of sensor-actuator co-located piezoelectric patches, using a genetic algorithm to solve the formulated discrete unconstrained minimisation problem. Design variables are element numbers in the finite element mesh where sensor-actuator pairs are to be applied, and the number of variables is chosen to be equal to the number of available patch pairs. A hybrid active-passive sandwich cantilever beam is used to verify the developed technique, and the optimal position of four sensor-actuator pairs has been determined for a free carbon fibre reinforced plate.

1

A.L. Araújo, C.M. Mota Soares, J. Herskovits, P. Pedersen, "Development of a finite element model for the identification of mechanical and piezoelectric properties through gradient optimisation and experimental vibration data", Composite Structures, 58, 307-318, 2002. doi:10.1016/S0263-8223(02)00192-7

2

J. Herskovits, P. Mappa, E. Goulart, C.M. Mota Soares, "Mathematical programming models and algorithms for engineering design optimization", Computer Methods in Applied Mechanics and Engineering, 194, 3244-3268, 2005. doi:10.1016/j.cma.2004.12.017

3

G. Yang, L.E. Reinstein, S. Pai, D.L. Carroll, "A new genetic algorithm technique in optimization of permanent 125-i prostate implants", Medical Physics, 25, 2308-2315, 1998. doi:10.1118/1.598460

4

ABAQUS 6.5, Hibbit, Karlsson and Sorensen Inc., Providence, RI, USA, 2005.

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