Random Matrices in Structural Acoustics

Abstract

This chapter is devoted to the predictions of complex structural–acoustic systems in the low and medium frequencies for which computational structural–acoustic models are required. The presentation is limited to a bounded structure coupled with bounded internal acoustic cavities. In order to simplify the presentation, the acoustic coupling of the structure with an unbounded external acoustic fluid is not considered here but can be taken into account without any difficulties. For complex systems, the main problem induced by such predictions is due to the incapacity of computational models (and of any another approaches) to represent a real complex system even if the model used is very sophisticated (multiscale modeling, very large number of degrees of freedom used in the finite element model, etc.). This problem is induced by the presence of both the system parameter uncertainties and the model uncertainties in the computational model and by the variabilities of the real complex system with respect to the design system. The objectives of this chapter is to model the uncertainties in the structural–acoustic computational model by using the random matrix theory and also to present a methodology to perform an experimental identification of the stochastic model and to present an experimental validation. The designed structural–acoustic system is the system conceived by the designers and analysts. A designed structural–acoustic system, made up of a structure coupled with an internal acoustic cavity, is defined by geometrical parameters, by the choice of materials, and by many other parameters.