The average radiation efficiency of a plate immersed in water with general boundary conditions

Abstract In this paper, the sound radiation characteristics of rectangular plates restrained with elastic boundaries immersed in water is studied with a unified approach. The Spectro-Geometric Method (SGM) is adopted by expressing the vibrating displacement of the structures into Fourier cosine series with additional functions. Hamilton principle is used to derive the strong coupling system in which the reaction between the vibration of the plate and the acoustic field is fully considered. The general boundary conditions are considered in the proposed method in which the boundaries of the structure are elastically restrained against springs. To fully investigate the influence of the restraints on the sound radiation from structures, the average radiation power and efficiency are analyzed for a flexible plate backed in a rigid baffle. Fourier transformation is adopted to reduce the quadruple integrals, which are encountered in calculating the sound power radiated from plate, into a series of single integrals which could be effectively calculated in a closed form. The accuracy and the convergence of the proposed modal is validated against the results in literatures. The effects of the elastic restraints on the sound radiation characteristics are studied by considering different combinations of the classical and elastic boundaries. The sound radiation from strips with variable aspect ratios is also analyzed.