Optimization and Parameter Estimation in Smart Viscoelastic Laminated Sandwich Structures

Recent developments on the optimization and parameter estimation in hybrid active-passive composite sandwich structures are presented. For this purpose, a mixed layerwise finite element model has been formulated, by considering a higher order shear deformation theory to represent the displacement field in the viscoelastic core and a first order theory for the displacement fields of the adjacent laminated and piezoelectric face layers. The model is based on an eight nodded plate/shell finite element, with 17 mechanical degrees of freedom per node, after imposing inter-layer displacement continuity, and 2 electric degrees of freedom per element. The complex modulus approach is used for the viscoelastic material behavior, and the dynamic problem is solved in the frequency domain, using frequency dependent material data for the core. Active control is applied using proportional displacement and negative feedback control laws. Damping maximization of passive, active and hybrid damping treatments is conducted, using as design variables the viscoelastic core thickness, the constraining elastic face laminae thicknesses, orientation fiber angles, as well as piezoelectric patch locations. The problems are solved using gradient optimization and/or nongradient algorithms as appropriate [1]. Identification of viscoelastic core material properties is also envisaged, where the inverse problem is formulated as a constrained optimization problem [2], by fitting the response of the numerical model to the corresponding experimental response of the structure, and considering specific parametric models for frequency dependent damping material behavior. Constraints are imposed on the design variables, arising from thermodynamic restrictions on isothermal linear viscoelasticity, and gradient based optimization techniques are used to solve the inverse problem. Both optimization and parameter estimation applications will be presented and discussed.