A wavenumber approach to modelling the response of a randomly excited panel, part I: general theory

Part I of this paper presents a self-contained analytical framework for determining the vibro-acoustic response of a plate to a large class of random excitations. The wavenumber approach is used, which provides an insight into the physical properties of the panel response and enables us to evaluate efficiently the validity of several simplifying assumptions. This formulation is used in Part II for predicting the statistical response of an aircraft panel excited by a turbulent boundary layer. In this paper, we first provide a general statement of the problem and describe how the spectral densities of the panel response can be obtained from an analysis of the system response to a harmonic deterministic excitation and a statistical model for the forcing field. The harmonic response of the system is then expanded as a series of the eigenmodes of the fluid-loaded panel and these fluid-loaded eigenmodes are approximated by a perturbation method. Then, we evaluate the conditions under which this series simplifies into a classical modal formulation in terms of the in vacuo eigenmodes. To illustrate the use of a wavenumber approach, we consider three examples, namely, the vibro-acoustic response of a panel excited by an incidence diffuse acoustic field, by a fully developed turbulent flow and by a pressure field which is spatially uncorrelated from one point to another. Convergence properties of the modal formulations are also examined