Piezoelectric active vibration control of damped sandwich beams

This work presents the design and analysis of the piezoelectric active control 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 accounted for through additional electrical degrees of freedom, condensed at the element level. The frequency dependence of the viscoelastic material properties 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 system 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 derivative feedback. To guarantee control feasibility and prevent piezoelectric material depoling, these algorithms are used in an iterative form to account for maximum control voltage. Parametric analyses of an actively controlled 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 their well-known spillover destabilizing effects are attenuated by the increase of stability margins provided by the viscoelastic damping. It is also shown that LQG controllers may perform as well as LQR ones. Moreover, the delay 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 control strategies for the active control of damped sandwich beams, accounting for frequency dependence of viscoelastic material properties, are some of the originalities of this work. The others are the analysis of the LQG algorithm and the state space real representation of complex modal reduced models for hybrid piezoelectric-active viscoelastic-passive vibration control which are presented for the first time. (C) 2001 Academic Press.