Nonlinear vibrations of a circular plate reinforced by ribs

Abstract

Abstract The behavior of a circular elastoplastic plate, consisting of a shell and reinforced ribs of a quadran-gular cross-section and under the action of dynamic loads, has been investigated. The rib sections are considered to be constant. The relationship between deformations and displacements is taken geometrically nonlinear, and between stresses and deformations in the form of Hooke’s law. Refined equations of the Timoshenko type are taken as resolving ones. It is believed that the vibrations of the plate are excited by a dynamic load acting on the surface of the plate. The solution of the differential equations for the vibrations of the plate, taking into account the elastoplastic properties of the shell materials and the reinforced ribs, is carried out by the finite difference method. The elastic and elastoplastic models are used to calculate the deflections of the central point and forces depending on the location of the ribs. In particular, it has been established that: when the plate is reinforced with one rib, the smallest deflection of the center point can be achieved when the rib is located in the middle of the radius; the proposed model and calculation method allow achieving the desired deflection value by varying the number of ribs.