Exact acoustical analysis of vibrating rectangular plates with two opposite edges simply supported via Mindlin plate theory

This study investigates acoustic radiation of rectangular Mindlin plates in different combinations of classical boundary conditions. A set of exact close-form sound pressure equations are given for the first time using the so-called Mindlin plate theory (a first-order shear deformation theory) for the plates having two opposite edges that are simply supported. The other two edges may be given any possible combination of free, simply-supported and clamped boundary conditions. It is assumed that no fluid loading occurs on the plate structure. In order to study the transverse vibration of moderately thick rectangular plates, the dimensionless equations of motion are derived based on the Mindlin plate theory. Structural–acoustic coupling is implemented for vibrating plate models. The radiation field of a vibrating plate with a specified distribution of velocity on the surface can be computed using the Rayleigh integral approach. The acoustic pressure distribution of the radiator is analytically obtained in its far field. To reveal the excellent accuracy of our exact acoustical solution, a comparison is first made with the existing data. Additionally, a few 3-D plots of the directivity pattern and their corresponding contour plots are illustrated for moderately thick rectangular plates with different boundary conditions. Finally, the influence of six possible combinations of boundary conditions, aspect ratios and thickness to length ratios on the sound pressure, frequency and critical distance parameters are examined and discussed in detail.