Determination of Maximum Deflection of Elastically Isotropic Plates with Combined Boundary Conditions Using Scaling Method

As a rule, the problems of statics and dynamics at physical and mechanical modelling of structures are considered separately. In this article, these two types of plate deformations (transverse bending and free vibrations) are considered in its interconnection. The functional dependence maximum deflection—vibration fundamental frequency for elastic isotropic plates of arbitrary form with a convex contour and combined boundary conditions (combination of simple support and clamping)—is obtained. We suggest the method of determination of maximum deflection of full-scale structures in the form of uniformly loaded plates by the vibration fundamental frequency of plate models in the unloaded state obtained experimentally. Applying regression analysis of the solutions which are presented in the scientific and reference literature, an approximating function w₀ − ω is plotted. It satisfies all variations of plates with a convex contour and arbitrary boundary conditions (combination of simple support and clamping around the contour) with the error (5–6)%. The article provides the examples of the proposed method application. It shows good accuracy.