Fast analytical approximations for the acoustic radiation impedance of rectangular plates with arbitrary boundary conditions

The radiation impedance is an essential parameter in analyzing the vibroacoustic response of the planar source. In order to calculate the acoustic radiation impedance of the rectangular plate with arbitrary boundary conditions, a unified approximate approach is proposed in this study. The displacement function of the plate is expressed in the form of a supplemented two-dimensional Fourier cosine series, which can be solved by the Rayleigh–Ritz method. The radiated acoustic field from the plate is further determined by the Rayleigh integrals. The coordinate transformation is performed twice to convert the quadruple integrals into simple integrals, significantly reducing the computational effort of the acoustic calculation. Regardless of the wavenumber or frequency, the proposed approach is theoretically accurate because no assumptions or approximations are involved in the mathematical process. Furthermore, the correctness of the formulas is validated by the results obtained from previous studies. Several numerical examples are performed using this approach, and the effects of boundary conditions on the modal radiation impedance are discussed.