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

TLDR: In this article, the radiation of sound from a baffled, rectangular plate with edges elastically restrained against deflection and rotation is analyzed, based on a variational method for the vibration of the plate, and assuming no fluid loading of the structure.

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 predic...