Abstract
The equations of motion based on Berger's hypothesis have been widely used in the non-linear free vibration analysis of elastic plates mainly because of the simplicity of these equations. A rational mechanical basis for these equations has not yet been found. In the present paper, the variationally derived in-plane boundary conditions are examined with specific reference to the plates with edges free of in-plane stress resultants. It is shown that for this boundary condition the Berger equations can result in zero non-linearity. A formal basis for the Berger equations is then critically discussed. Approximate modal equations governing the non-linear, free, flexural vibrations of a few plate geometries are presented and compared with the von Kármán results. The numerical study reveals that the Berger equations do not yield consistently accurate results, and the results show an entirely different pattern of deformation. These observations may justify certain reservations regarding the general applications of the Berger equations.
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