Analytical modelling of the structural acoustic vibrations in a paneled box

This paper presents a viable modal approach to the modeling of broadband structural-acoustic vibrations in a paneled box. The active control of broadband structural-acoustic vibrations is a topic of current research. For a robust practical solution to this problem, a thorough understanding of the physics of the problem is needed. The model needs to be flexible to allow changes in the types, number and locations of actuators and sensors. The modal approach to modeling offers an efficient solution, since it enables quick construction of the model once the basic modes and structural-acoustic coupling have been determined. The issue of model size is also addressed. Standard model reduction techniques in the case of very large systems suffer from numerical conditioning problems and are also highly affected by the modal damping and frequency values, so that the higher modes tend to be dropped out in the reduced model. To make the model reduction insensitive to damping (which is never correctly known), a model reduction procedure is presented which uses a modal measure to determine the contribution of the different modes to the input-output map. The proposed measures are computed in a straightforward manner and do not suffer from numerical conditioning problems. The proposed model reduction procedure is found to work extremely well in reducing the model size accurately. Further, the model reduction procedure offers insight into possible control solutions to the broadband active control problem.