IOP PUBLISHING SMART MATERIALS AND STRUCTURES Smart Mater. Struct. 16 (2007) 2159–2168 doi:10.1088/0964-1726/16/6/018 Optimization of active–passive damping treatments using piezoelectric and viscoelastic materials M A Trindade Department of Mechanical Engineering, S˜ ao Carlos School of Engineering, University of S˜ ao Paulo, Avenida Trabalhador S˜ ao-Carlense, 400, S˜ ao Carlos-SP, 13566-590, Brazil E-mail: trindade@sc.usp.br Received 2 April 2007, in final form 30 July 2007 Published 8 October 2007 Online at stacks.iop.org/SMS/16/2159 Abstract Several active–passive damping treatments using viscoelastic and piezoelectric materials have been studied in the last decade. The main motivation of such hybrid damping mechanisms is that they combine the reliability, low cost and robustness of viscoelastic damping treatments with high-performance, modal selective and adaptive piezoelectric active control. However, active–passive damping performance is highly dependent on the relative positions of viscoelastic and piezoelectric materials. This work presents a geometric and topological optimization of active–passive damping treatments, consisting of a viscoelastic layer, a constraining layer, a spacer layer and a set of piezoelectric actuators. The modelling is performed using a piezoelectric sandwich/multilayer beam finite element model in which the viscoelastic material’s frequency dependence is accounted for using the anelastic displacement fields model. The resulting model is then reduced using a two-step modal reduction and applied to a limited-input optimal control strategy to evaluate the resulting active–passive modal damping factors. A genetic algorithm based optimization technique combined with an aggregated weighted minimum–maximum approach for a multiobjective optimization is used, aiming for the maximization of active–passive damping and minimization of weight added to the structure. Results show that a considerable improvement of damping performance is achievable with a controlled increase in the mass of the structure. (Some figures in this article are in colour only in the electronic version) 1. Introduction Several research works published in the last decade have shown the advantages of combining standard free layer and constraining layer viscoelastic damping treatments with some type of distributed active control to reduce structural vibration amplitudes. The viscoelastic damping treatments offer a reliable, low-cost and robust solution for vibration damping, and they are already widely used in several industries. On the other hand, studies on the application of distributed active control using piezoelectric actuators for real structures has seen a considerable growth in recent years. Purely active control can provide high-performance, modal selective and adaptive solutions for narrow frequency ranges. Aiming to improve passive damping performance or reduce the required weight increase, a number of research groups proposed hybrid active–passive damping treatment configurations combining both viscoelastic and piezoelectric materials in the structural design. Depending on the relative positions of the passive damping layers and the active piezoelectric actuators, the active and passive damping mechanisms can work separately or simultaneously. The most studied configuration consists of replacing or augmenting the elastic constraining layer of a passive constrained layer (PCL) damping treatment by an active piezoelectric actuator, leading to the so-called active 0964-1726/07/062159+10$30.00 © 2007 IOP Publishing Ltd Printed in the UK 2159