Flexural Vibrations of a Plate under Changes in the Mean Pressure on Its Surfaces

Abstract—The influence of the mean excess pressure on a cylindrical static bend and vibrations of a plate is studied. Increasing and decreasing this pressure lead to a decrease and increase in deflection, respectively. In the first case, the plate shape stabilizes under the action of longitudinal forces, while in the second case, destabilization takes place. The critical value of the mean pressure is determined. The dynamic modes of plate deformation under a sharp increase and decrease in pressure are analyzed. In the first case, vibrations with increased frequency are excited, while in the second case, the excited vibrations have a reduced frequency compared to the natural frequency of the unloaded plate. For deep evacuation, an exponential increase in deflection with time is observed. A method for solving the problem for complex pressure changes has been developed.