A compressional-shear model for vibration control of beams with active constrained layer damping

In the modeling of the active constrained layer damping (ACLD) structures, the transverse displacements of the constraining layer and the host structures are usually assumed to be compatible. However, when performing active control, even a small difference between the transverse displacement of the constraining layer attached with actuator and that of the host structures bonded with sensor may destabilize the closed-loop control system. In order to understand the effect of incompatible transverse displacements, a model for the beam with ACLD in which both compressional vibration and shear damping are considered, is developed. In this model, the viscoelastic layer is modeled to carry not only the shear strain but also the peel strain. In addition, a thorough solution scheme to obtain the eigenvalues and frequency response of the closed-loop controlled beam is also given based on multiple shooting method. The effects of the compressional vibration on passive and active control are investigated through simulation examples. It is found that the compressional vibration can significantly affect the frequencies and damping ratios of higher-order modes of an actively controlled beam and may even destabilize the active control.