Effect of Ambient Pressure and Density on the Spectrum of Vibration Frequencies of Rectangular Plates Hinged along the Contour

The frequency spectrum and modes of bending vibrations of rectangular plates in contact with a liquid or gas are determined. An expression is obtained for the distributed transverse load on a plate hinged along the contour. The surfaces of the plate are in contact with a medium of different density and pressure. The medium can be both compressible and incompressible. The effects of the average pressure, the curvature of the middle surface, and the added mass of the gas medium on the bending are determined.