The radiation of sound from a baffled, rectangular plate with edges elastically restrained against deflection and rotation is analyzed. The elastic constants along the contour can be varied to reproduce simply supported, clamped, free, or guided edges as limiting cases. The formulation is based on a variational method for the vibration of the plate, and assumes no fluid loading of the structure. The elastic boundary conditions appear in the Hamiltonian of the plate through a dynamic contribution, which is expressed in terms of nondimensional edge parameters. The extremalization of the Hamiltonian is achieved using a Rayleigh–Ritz method, and both the free vibrations and the forced vibrations of the plate are presented. The radiation of sound from the plate is analyzed in the far field, and is calculated from one-dimensional Fourier transforms. Numerical results are presented for the radiation efficiency of modes of simply supported, clamped, free, and guided plates. The values found agree well with predictions of Wallace in the simply supported case, and of Gomperts in the guided case. It is found that a low deflection stiffness at the edges decreases the radiation efficiency of the elastic modes in a spectacular manner. The radiation efficiency of the rigid modes of the plate is derived analytically in low frequencies. It is seen that, when rigid motion of the plate is permitted, it is responsible for almost all the acoustical power radiated. The new case of a plate which is locally clamped along its four edges is also presented.

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Sound transmission loss through double panels is studied with a patch-mobility approach. An overview of the method is given with details on acoustic and structural patch mobilities. Plate excitation is characterized by blocked patch pressures that take into account room geometry and source location. Hence, panel patch velocities before coupling can be determined and used as excitation in the mobility model. Then a convergence criterion of the model is given. Finally, transmission loss predicted with a patch-mobility method is compared with measurements.

The theoretical approach presented in this paper allows SEA coupling loss factors for subsystems to be modelled with FEM. It is then possible to take into account the complicated substructure that can be encountered in practical industrial application. The technique relies on the basic SEA relation for coupled oscillators and the use of dual modal formulation to describe vibration of coupled subsystems. With this approach, the boundary conditions of uncoupled subsystems are clearly de"ned and, as assumed in SEA, no modal coupling exists in a subsystem. Modes of two di!erent subsystems are coupled together by gyroscopic elements and the coupling strength is related to eigenfrequencies of the uncoupled subsystems and mode shapes through the interaction modal works. A general expression for CLF has been obtained, and it allows CLF to be determined only from the knowledge of the modes of the uncoupled subsystems and the modal damping. Finite element model can be used to calculate the modal information in the case of complex substructures. It is possible to treat the case of heterogeneous subsystems having three-dimensional vibration motions without di$culty. Contrary to the classical approach which is based on SEA inverse matrix and numerical experiments which necessitate calculations of subsystem energies for the coupled structures for many excitation points, this technique calculates CLF directly from the governing equations without solving them. In a companion paper, the present approach is applied to a simple example to illustrate and validate the approach.

International audienceIn order to enlarge the application field of Statistical Energy Analysis (SEA), a reformulation is proposed. The model described here, Statistical modal Energy distribution Analysis (SmEdA), does not assume equipartition of modal energies contrary to classical SEA. Theoretical derivations are based on dual modal formulation described in [1,2] for the general case of coupled continuous elastic systems. Basic SEA relations describing power flow exchanged by two oscillators are used to obtain modal energy equations. They permit to determine modal energies of coupled subsystems from the knowledge of modes of uncoupled subsystems. The link between SEA and SmEdA is established and render possible to mix the two approaches: SmEdA for subsystems where equipartition is not verified and SEA for other subsystems. Three typical configurations of structural couplings are described for which SmEdA improves energy prediction compared to SEA: (a) coupling of subsystems with low modal overlap. (b) coupling of heterogeneous subsystems. (c) case of localised excitations.The application of the proposed method is not limited to academic structures, but could easily be applied to complex structures by using finite element method (FEM). In this case, FEM are used to calculate the modes of each uncoupled subsystems; these data are then used in a second step to determine modal coupling factors necessary to SmEdA to modelise the coupling

A method to couple acoustic linear problems is presented in this paper. It allows one to consider several acoustic subsystems, coupled through surfaces divided in elementary areas called patches. These subsystems have to be studied independently with any available method, in order to build a database of transfer functions called patch transfer functions, which are defined using mean values on patches, and rigid boundary conditions on the coupling area. A final assembly, using continuity relations, leads to a very quick resolution of the problem. The basic equations are developed, and the acoustic behavior of a cavity separated in two parts is presented, in order to show the ability of the method to study a strong-coupling case. Optimal meshing size of the coupling area is then discussed, some comparisons with experiments are shown, and finally a complex automotive industrial case is presented.

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