Piezoelectric active vibration control of damped sandwich beams

This work presents the design and analysis of the piezoelectric active cont rol of damped sandwich beams. This is done using a specific finite element, able to handle sandwich beams with piezoelectric laminated surface layers and viscoelastic core. The piezoelectric direct and converse effects are ac counted for through additional electrical degrees of freedom, condensed at the element level. The frequency dependence of the viscoelastic material pr operties is modelled using additional dissipative variables resulting from an anelastic displacement fields model. A complex-based modal reduction is then proposed and an equivalent real representation of the reduced-order sy stem is constructed. The control design and performance are then evaluated using three control algorithms applied to the reduced-order model, namely, linear quadratic regulator (LQR), linear quadratic gaussian (LQG) and deriv ative feedback. To guarantee control feasibility and prevent piezoelectric material depoling, these algorithms are used in an iterative form to accoun t for maximum control voltage. Parametric analyses of an actively controlle d damped sandwich beam indicate that LQR controllers improve some selected modal dampings, while retaining the passive damping of uncontrolled modes. Derivative feedback controllers are less effective than an LQR one, but the ir well-known spillover destabilizing effects are attenuated by the increas e of stability margins provided by the viscoelastic damping. It is also sho wn that LQG controllers may perform as well as LQR ones. Moreover, the dela y effect induced by the state estimation of LQG associated with the passive attenuation lead to a damping performance similar to that of LQR with less control voltage. The parametric analyses and the comparative study of cont rol strategies for the active control of damped sandwich beams, accounting for frequency dependence of viscoelastic material properties, are some of t he originalities of this work. The others are the analysis of the LQG algor ithm and the state space real representation of complex modal reduced model s for hybrid piezoelectric-active viscoelastic-passive vibration control wh ich are presented for the first time. (C) 2001 Academic Press.