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In this work a finite element model is developed for vibration analysis of active-passive damped multilayer sandwich plates, with a viscoelastic core sandwiched between elastic layers, including piezoelectric layers. The elastic layers are modelled using the classic plate theory and the core is modelled using the Reissener-Mindlin theory. The finite element is obtained by assembly of N ''elements'' through the thickness, using specific assumptions on the displacement continuity at the interfaces between layers. The lack of finite element plate-shell models to analyse structures with passive and active damping, is the principal motivation for the present development, where the solution of some illustrative examples and the results are presented and discussed.