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.

This paper discusses the prediction of the low frequency diffuse field transmission loss through double-wall sound barriers with elastic porous linings. The studied sound barriers are made up from a porous-elastic decoupling material sandwiched between an elastic skin and a septum. The prediction approach is based on a finite element model for the different layers of the sound barrier coupled to a variational boundary element method to account for fluid loading. The diffuse field is modeled as a combination of uncorrelated freely propagating plane waves with equal amplitude, no two of which are traveling in the same direction. The corresponding vibroacoustic indicators are calculated efficiently using a Gauss integration scheme. Also, a power balance is presented to explain the dissipation mechanisms in the different layers. Typical results showing the effects on the transmission loss of several parameters such as the septum mass, the decoupling porous layer properties and the multi-layer mounting conditions are presented.

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An efficient modal approach to characterize the diffuseness of the sound field in a rectangular room is presented. Using two simple descriptors, the correlation function and the spatial uniformity of the pressure field, a practical and convenient tool is proposed to study the diffuse field in the room. A precise criterion has been given in terms of the least permissible number of room modes to achieve an adequate diffusion. It has been shown that the criterion is in great accordance with the well-known “Schroeder frequency” limit for the diffuse field. Detailed calculations of the correlation function are presented to show the importance of the Δk/k correction terms to the well-known sin(kR)/kR prediction. A new closed form for the correlation function is thus derived. A discussion about the importance of having more than one descriptors is also presented. It is shown that a diffuse field can be established in a room with strong modal behavior under certain assumptions.

The radiation of sound from a point-driven circular plate into a hard-walled cylindrical enclosure is investigated. Emphasis is given on studying the effects of the boundary conditions of the plate, which are modeled as a continuous distribution of edge springs acting against both the deflection and the rotation of the contour of the plate. With this model, both classical and intermediate boundary cases can be simulated by adjusting the elastic stiffness of the springs. A coupled acoustoelastic formulation is developed following a variational approach, with the use of hard-walled cavity modes. In the analysis, the full interaction between the structure vibration and the internal cavity sound pressure is considered. Numerical results indicate that a significant reduction in noise inside the cavity can be obtained for a relatively wide frequency range by completely relaxing the translational support (zero deflection stiffness) of the plate. This is mainly due to a weakening of the modal radiation efficiency of the flexural modes of the plate. With an increase of the deflection stiffness on the contour of the plate, this beneficial frequency range is shifted to higher frequencies. It is hoped that the findings of the present work will be useful for practical predictions of airplane cabin noise emitted by the rear pressure bulkhead, as well as for noise control in some aerospace structures and mechanical systems involving cylindrical-shaped cavities.

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