A new approach for free vibration analysis of a system of elastically interconnected similar rectangular plates

A new procedure is proposed to ease the analyses of the free vibration of an elastically connected identical plates system with respect to Kirchhoff plate theory. A structure of n parallel, elastically connected rectangular plates is of concern, whereby the motion is explained by a set of n coupled partial differential equations. The method involves a new change in variables to uncouple equations and form an equal system of n decoupled plates, while each is assumed to be elastically connected to the ground. The differential quadrature method is adopted to solve the decoupled equations. To unravel the original system, the inverse transform is applied. Decoupling the equations enables one to solve them based on the solution methods available for a single plate system. This also diminishes the computational costs of such problems. By considering different boundary conditions, a case study is run to present the method and to validate the results with its counterparts, for which excellent agreement is observed. Assessing the influence of dimensionless thickness, aspect ratio, and stiffness coefficients on the frequencies reveals the different effects of them at the low order of dimensionless natural frequencies in comparison with high orders and for different boundary conditions.