Plates are applied to a wide array of structural applications of varying complexity. Each application requires rigorous analysis to determine the viability of the proposed model. One such application involves modeling a larger structure as a collection of smaller flat plates connected at the plate boundaries. Previous research into these types of structures has led to varying levels of accuracy. It has been dependent on the applications and assumptions involved. To improve the accuracy of these types of structures in a more general context, we propose expanding on current models of coupled plates by modeling the plates using Mindlin plate theory. We analyze the vibration of the improved model with general elastic boundary conditions, point supports and coupling conditions using the Fourier series method and finite element software. When the Fourier series method is applied directly, continuity issues arise at the plate coupling boundaries. To resolve these issues, the Fourier series solution of the vibration displacements is amended to include auxiliary functions. This improved coupled plate model is analyzed and numerically simulated for a variety of elastic boundary conditions and coupling conditions. The numerical results are produced using the Fourier series method and a finite element solution to demonstrate the validity of the improved coupled plate model.

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Based on Kirchhoff plate theory and the Rayleigh-Ritz method, the model for free vibration of rectangular plate with rectangular cutouts under arbitrary elastic boundary conditions is established by using the improved Fourier series in combination with the independent coordinate coupling method (ICCM). The effect of the cutout is taken into account by subtracting the energies of the cutouts from the total energies of the whole plate. The vibration displacement function of the hole domain is based on the coordinate system of the hole domain in this method. From the continuity condition of the vibration displacement function at the cutout, the transition matrix between the two coordinate systems is constructed, and the mass and stiffness matrices are completely obtained. As a result, the calculation is simplified and the computational efficiency of the solution is improved. In this paper, numerical examples and modal experiments are presented to validate the effectiveness of the modeling methods, and parameters related to influencing factors of the rectangular plate are analyzed to study the vibration characteristics. KEYWORDSRectangular plate with cutouts; the independent coordinate coupling method; elastic boundary conditions; free vibration analysis