The vibration and post-buckling of geometrically imperfect,simply supported,rectangular plates under uni-axial loading,part I: Theoretical approach

The work described in this paper constitutes the theoretical part of a theoretical and experimental study of the post-buckling and vibration of simply supported rectangular plates having slight initial curvature (geometrical imperfection) and subject to uni-axially applied, in-plane, compressive loads. The experimental part, and the comparison with theoretical predictions, is given in a second paper. The Rayleigh-Ritz approach, with a deflection function formulation for both the in- and out-of-plane behaviour of the plates, is used since this permits the convenient modelling of various types of in-plane boundary conditions, including those encountered in the experimental study. A concept of connection coefficients, introduced to reduce the computational effort involved, is described. In order to illustrate the applicability of the theoretical approach, a number of square plates having various sets of in-plane boundary conditions and degrees of initial imperfection are treated. Graphical results are presented showing the variation of the lateral central deflection and the fundamental natural frequency of vibration with applied in-plate loads varying from zero to several times the lowest critical buckling load. Where possible, comparison is made with values available in the literature and excellent agreement is achieved. The results presented appear to suggest that an approximately linear relationship exists between a load-frequency parameter and the central deflection of the plates considered, for a substantial in-plane loading range.