On the active-passive hybrid control actions of structures with active constrained layer treatments

This paper is concerned with the analysis of active and passive hybrid actions in structures with active constrained damping layers (ACL). A system model is derived via Hamilton's Principle, based on the constitutive equations of the elastic, viscoelastic, and piezoelectric materials. The model converges to a purely active piezotronic system as the thickness of the viscoelastic material (VEM) layer approaches zero. A mixed Galerkin-GHM (Golla-Hughes-McTavish) method is employed to discretize and analyze the model in time domain. With an LQR (linear quadratic regulator) optimal control, the effects of the active constrained layer configuration on the system vibration suppression performance and control effort requirements are investigated. Analysis illustrates that the active piezoelectric action-with proper feedback control will always enhance the damping ability of the passive constrained layer. When compared to a purely active configuration, while the viscoelastic layer of the ACL treatment will enhance damping, it will also reduce the direct control authorities (active action transmissibility)from the active source to the host structure. Therefore, whether the ACL treatment is better than a purely active configuration depends on whether the effect of damping enhancement is greater than that of transmissibility reduction caused by the VEM layer. The significance of these effects depends very much on the viscoelastic layer thickness and material properties. With some parameter combinations, the ACL configuration could require more control effort while achieving less vibration reductions compared to a purely active system. Through analyzing the performance and control effort indices, the conditions where this active-passive hybrid approach can outperform both the passive and active configurations are quantified Based on this study, design guidelines can be set up to effectively integrate the host structure with the piezoelectric and viscoelastic materials, such that a truly beneficial active-passive hybrid control system could be achieved.