Control of harmonically driven resonating compliant structures using local structural modifications

The motion amplitude of a harmonically driven compliant structure is maximized if the driving frequency equals one of the structural resonance frequencies. For the effective use of resonating compliant structures, control of the eigensolutions, i.e., eigenfrequencies and eigenmodes, is often required. This work shows a design methodology in which eigenproblem sensitivity is used in a systematic way to design the most effective locations to apply local structural modifications for a required change in the eigensolutions. By applying control patches at these locations the power requirements are minimized. The modal basis of the structure is used as the preferred basis which leads to valuable insights in the possibilities and limitations of controlling specific eigensolutions. The influence on the eigensolutions due to the mechanical properties of the attached inactive control actuators is separated from the influence due to the active actuation of the control actuators. Whether or not a control actuator is actively actuated depends on the desired control state. Furthermore, it is argued that nearly repeated eigenfrequencies contribute to the effective control of eigenmodes. A simple compliant structure is used to demonstrate the potential of the presented design methodology. In this example, the uncontrolled eigensolutions are forced into different, independent control states using effectively distributed control actuators. Keywords: Resonance, Compliant Structures, Eigenproblem Sensitivity, Local Structural Modifications, Control States, Control patches