Creating Nodes at Selected Locations in a Harmonically Excited Structure Using Feedback Control and Green’s Function

Abstract

The paper deals with designing a control force to create nodal point(s) having zero displacements and/or zero slopes at selected locations in a harmonically excited vibrating structure. It is shown that the steady-state vibrations at desired points can be eliminated using feedback control forces. These control forces are constructed from displacement and/or velocity measurements using sensors located either at the control force position or at some other locations. Dynamic Green’s function is exploited to derive a simple and exact closed from expression for the control force. Under a certain condition, this control force can be generated using passive elements such as springs and dampers. Numerical examples demonstrate the applicability of the method in various cases.