An active vibration absorber for a flexible plate boundary-controlled by a linear motor

A long, narrow flexible plate subjected to cyclic disturbances at the midsection is regulated by a linear motor at the boundary. Oscillations at the midsection will be eliminated while the rest of the plate is allowed to swing in a way as to counteract the external force. The control design is based on a virtual passive approach without referring to the detailed mathematical model. A vibration absorber integrating the flexible plate with a combination of passive elements attached to the boundary is first devised. Rather than built with hard physical devices, these passive elements including mechanical springs, dampers, and masses are emulated by the linear motor with a suitable feedback law. The feedback signal is the boundary displacement from an LVDT sensor. Numerical simulations illustrate how a node is developed in the middle of the plate while the rest of the structure tends to a harmonic motion. Experimental results confirm the effectiveness of the control scheme.