A general formulation for the sound radiation from rectangular, baffled plates with arbitrary boundary conditions

Abstract

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.

Sound radiation from perforated plates

“…In mode ( modes. However, the modal resonance frequency for mode (21,1) is 7.6 kHz, which is much lower than the resonance frequency for mode (20,20), i.e. 18.6 kHz.…”

“…Later in [21] it was found that only one set of trial functions was required to represent the plate displacement. Berry et al [20] found that in low-order modes up to the mode (2,2), the simply supported plate has a slightly higher radiation efficiency than that of the clamped plate. For all other modes, the opposite situation applies with a maximum factor of 2.5 (4 dB).…”

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“…The excitation is very often asymmetric in the real vibrating systems and it is very useful to find some asymptotic and approximate formulae for the modal quantities necessary to compute the acoustic power, the acoustic pressure and the structure's vibration velocity including the fluid loading. So far, a number of such formulae have been presented for vibrating circular and rectangular membranes and plates using several approximate methods [1][2][3][4][5][6][7][8][9]. The results obtained by using the exact solutions for the free vibrations have been presented in a few studies [10][11][12].…”

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