Feedback control of wave propagation in a rectangular panel, Part 1: Theoretical investigation of fundamental characteristics

Abstract

This study presents the feedback control of flexural waves propagating in a rectangular panel. The objective of this paper (part 1) is to theoretically investigate the fundamental properties of the feedback wave control system. First, a transfer matrix method in the Laplace domain is introduced which is based on a wave solution of a rectangular panel. This is followed by the derivation of the characteristic equation and the feedback control laws for absorbing the reflected waves. Then, from a viewpoint of numerical simulations, the control performance of the proposed method is clarified. It is found that the reflected wave absorbing control enables inactivation of vibration modes since standing waves which cause resonant phenomena disappear from the structural vibration. Finally, the stability verification of the proposed control system is conducted using Nyquist diagram. It is shown that although the controller has unstable poles in some cases, the nominal control system is stable irrespective of whether the collocation holds or not. Furthermore, it is clarified that a wave-absorbing control system becomes robust for the parameter fluctuation if the uncontrolled region does not exist.