Global Stabilization of the 1-Periodic Response of a Beam With One-Sided Spring

摘要

Global stabilization of the 1-periodic response of a harmonically excited beam with one-sided spring is used to reduce vibration amplitude with small control effort. Control is based on linear error feedback at a single position on the beam. Linear error feedback changes the error dynamics by creating bifurcations. These bifurcations determine the necessary condition needed to globally stabilize the 1-periodic response. Once stabilized, the entire beam converges to the 1-periodic response while the control force converges to zero because the 1-periodic response is a solution of the uncontrolled system.