Damping Behavior Of Cantilevered Structronic Systems with Boundary Control

Abstract

Distributed control of cantilever distributed systems using fully distributed piezoelectric layers has been investigated for years. The equivalent control actuation is introduced at the free end of the cantilever distributed systems, and the control action is equivalent to a counteracting control moment determined by the geometry, material properties, sensor signal, and control laws. In the negative proportional velocity feedback, the control effect is proportional to the feedback voltage and the controlled damping ratio usually exhibits linear behavior, if the feedback voltage is low. In this study, nonlinear damping behavior and an (equivalent) boundary changes of cantilever beams and plates with full-range feedback voltages are studied. Analytical solutions are compared with finite element simulations and experimental data. Studies suggest that the controlled damping ratio increases at low control gains and it decreases at high control gains induced by the boundary control moment. Furthermore, due to the highly constrained boundary control moment at high gains, the original fixed-free boundary condition can be approximated by an equivalent fixed/sliding-roller boundary condition.