The transverse vibration of Mindlin rectangular plates with internal elastic supports and arbitrary boundary supports

Rectangular plates on internally distributed column supports are widely used in civil and ship structures, such as floating rafts, solar panels, and bridge decks. In this investigation, the transverse vibration of rectangular plates with internal rectangular supports and general elastically restrained boundary conditions are solved using the Rayleigh–Ritz technique. The Mindlin plate theory is adopted, and stiffness matrices of the inner support are solved by using higher-order Gauss–Legendre quadrature. The admissible functions are the combination of cosine series and auxiliary sine functions, which can apply to any elastically restrained boundary condition. Through convergence and comparison studies, the admissible functions with four terms of sinusoidal auxiliary functions have better convergence, and the obtained frequency parameters and mode shapes are consistent with those from finite element analysis and the literature. Finally, numerical results of rectangular plates with internal supports of different aspect ratios and different positions are investigated. The results show that the effect of internal support stiffness on free vibration frequencies and modal shape of plate cannot be ignored. According to the parameters studies, the change of the aspect ratio of the internal support has little effect on the frequencies, and however, it has some effect on the mode shapes, especially the higher-order mode shapes. These findings can serve as benchmark solutions for future studies.