Vibro-acoustic analysis of Mindlin rectangular plates resting on an elastic foundation

This study investigates the acoustic radiation of rectangular Mindlin plates in different combinations of classical boundary condition. A set of exact close-form sound pressure equations is given for the first time, using the so-called Mindlin plate theory (a first-order shear deformation theory), for 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 condition. It is assumed that mechanical in-plane 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. Additionally, the influence of six possible combinations of boundary condition, foundation parameter, loading case, aspect ratio and thickness ratio, on the sound pressure is examined and discussed in detail.