Active control of noise in plate-cavity coupled systems using the pole placement method

Abstract

Structure-acoustic coupled systems have received great attention in engineering, and a typical representative is a plate coupled with a cavity. The sound in the cavity is excited by the vibration of the plate and when there is strong coupling between the acoustic modes of the cavity and the vibrational modes of the plate, the sound pressure can be enhanced dramatically. In this paper, active control based on the pole placement method is used for the first time to reduce the noise in a plate-cavity coupled system. The principle of the pole assignment is that the poles of a system represent the system’s dynamical behaviour, and their assignment allows one to modify the response of the system using sensors and actuators. In this work, the usage of pole assignment to modify the dynamics of the plate is theoretically derived, and the resulting sound in the cavity is analytically calculated by solving a coupled matrix equation. To access the performance of the pole placement method in reducing the noise in the coupled system, three example cases are considered. The first is a local control case which uses a single actuator to control the first two modes of the plate in order to attenuate the resulting sound in the cavity. The second case is imposing global control by using two actuators to modify the first four modes of the plate, weakening the strong interaction between the pate and the cavity by shifting their natural frequencies away from each other. The third is applying uncontrollability conditions to retain particular modes when the control method is applied. The analytical results show that the pole placement method can be effective to control both the vibration and the vibro-acoustics in the plate-cavity coupled system. The finite element (FE) method is used to validate the analytical models. The FE predictions show good agreement with the analytical results. The pole placement method is shown to be effective in controlling the noise in this plate-cavity coupled system, and there is the potential to extend the method to more complex structure-acoustic coupled systems.