Free vibration of rectangular plates with internal column supports

A direct method is proposed to derive the exact solution for the free vibration of a thin rectangular plate with two opposite edges simply supported and with internal column supports. Considering the compatibility of displacements and rotations between the plate and the columns, the coupled vibration of a plate–column system is derived. The accuracy and correctness of the present method are demonstrated through the comparison of the results obtained from the proposed method and from finite-element analysis. Then the effects of column sizes and column models on the natural frequencies of a plate–column system are investigated in detail. A parametric study is focused on fully simply supported rectangular plates with a single internal column. It is shown that the effect of column flexibility in plate–column structures should be considered. The solution provided in the paper is general and includes several particular solutions for fixed point-supports, pinned point-supports and elastic point-supports. Results with high accuracy have been obtained and these can be used as the benchmark for the further investigation and for other approximate methods.