Buckling and Vibration of a Stepped Plate

Abstract

This study analyses the elastic stability and free vibration of a simply supported stepped plate under combined loading conditions defined by the parameter α. Mathematical identification of these phenomena has been made using Levy's method as implemented in the conditions of equivalent fictitious load. The buckling coefficient k and the frequency parameter λ of the stepped plate were verified according to literature sources. Influential parameters of stability and the free vibration of the stepped plate under combined load were identified. It has been concluded that the buckling coefficient primarily depends on the relative thickness Δt, while the frequency parameter λ was significantly affected by the position of discontinuity Δb. Pure bending (α=2) induces several buckling modes for the same plate geometry with respect to uniform compression (α=0), thus creating a considerable technological stability reserve, particularly at higher discontinuities. Formulation of the frequency parameter enables us to choose the optimum geometry with minimal susceptibility to the appearance of free vibration in the plate.