Effect of debonding in active constrained layer damping patches on hybrid control of smart beams

A new model for a smart beam with a partially debonded active constrained layer damping (ACLD) patch is presented, and the effects of the debonding of the ACLD patch on both passive and hybrid control are investigated. In this model, both shear and compressional vibrations of the viscoelastic material (VEM) layer are considered. The moment inertia and the transverse shear effect are also taken into account based on the Timoshenko’s beam theory. The adhesive layer between the host beam and the piezoelectric sensor patch is modeled as an elastic load transferring media. The debonding of the ACLD patch is approximated by removing the VEM between the constraining layer and the host beam in the debonding region, and the continuity conditions are imposed based on displacement continuity and force balance. A modal velocity observer-based modal control scheme is also given to perform the active modal control of the beam. In order to examine the effects of part debonding of the ACLD patch, the characteristic equation of the beam treated with an ACLD patch is derived. The simulation example results show that an edge debonding of the ACLD patch can significantly affect both passive and hybrid control. It is also found that the additional mode induced by the debonding has unique effects on the modal damping ratios and frequencies of both open-loop and closed-loop system.