Vibroacoustic analysis of rectangular plates with elastic rotational edge restraints

This investigation deals with the vibration of and the acoustic radiation from a simply supported rectangular plate with elastic restraints against edge rotations. The displacement of the plate is first sought as a series expansion in terms of the beam functions. Each of the beam functions is then expressed as the linear combination of a Fourier sine series and a complementary sufficiently smooth function that is introduced to ensure and improve the convergence of the Fourier series expansion. To facilitate the acoustic analysis, the plate displacement is eventually simplified to a standard Fourier sine series. The modal and acoustic characteristics of square plates are studied for different restraining stiffnesses and configurations. It is shown that the modes of the restrained plates can be considerably different from those in the simply supported case, so are the corresponding modal radiation efficiencies. The proposed method is generally applicable to rectangular plates elastically restrained along any edge(s), and the acoustic calculations are valid for an arbitrary acoustic or structural (modal) wave number.