Keywords: finite elements, piezoelectric actuators, velocity feedback, viscoelastic material.

In this paper a simple and efficient finite element model is used for the damping optimization of multilayer sandwich plates, with a viscoelastic core sandwiched between elastic layers, including piezoelectric layers. The elastic layers are modelled using the classical plate theory and the core is modelled using Reddy's third-order shear deformation theory. The finite element formulation is obtained by the assembly of N non-conforming triangular finite elements through the thickness, using specific assumptions on the displacement continuity at the interfaces between layers [1]. The free vibration response of damped multilayer sandwich plate structures is obtained by solving an eigenvalue problem to obtain the fundamental natural frequency and corresponding modal loss factor. An hysteretic model is considered for damping, using the complex modulus approach.

The optimization is conducted in order to maximize the fundamental modal loss factor, using gradient based algorithms, and afterwards, considering steady state harmonic motion, the analysis is conducted in the time domain to obtain the plate response. The design variables are the orientation of the composite elastic face layers and the thicknesses of the elastic face layers as well as the thickness of the viscoelastic core. Constraints are imposed on the total mass of the structure as well as on the maximum displacement.

The model is applied in the solution of some illustrative examples and the results are presented, discussed and compared with solutions obtained using an alternative numerical model and optimization techniques [2]. Results show that the present technique is reliable for improving substantially modal loss factors for beam and plate type sandwich structural elements.

1

J.S. Moita, A.L. Araújo, P.G. Martins, C.M. Mota Soares, C.A. Mota Soares, "Analysis of Active-Passive Plate Structures using a Simple and Efficient Finite Element Model", Mechanics of Advanced Materials and Structures, 18, 159-169, 2011. doi:10.1080/15376494.2010.496062

2

A.L. Araújo, P. Martins, C.M. Mota Soares, C.A. Mota Soares, J. Herskovits, "Damping Optimization of Viscoelastic Laminated Sandwich Composite Structures", Structural and Multidisciplinary Optimization, 39, 569-579, 2009. doi:10.1007/s00158-009-0390-4

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