Dynamic analysis of rectangular cut-out plates resting on elastic foundation

A finite element method using a 9-node isoparametric plate bending element, incorporating the effects of transverse shear based on the first-order shear deformation theory, is proposed for the free vibration analysis of rectangular cut-out plates resting on an elastic foundation. The elastic foundation is modeled on the Winkler and the Pasternak type, and equations of motion are obtained using the principle of virtual work. To account for the parabolic strain variation through the thickness, a shear correction factor of 5/6 is used, and the effect of rotary inertia has been included in the formulation. The present formulation is compared with established results obtained using analytical methods, with and without rotary inertia, and the max variation observed is 2.24% without rotary inertia and 0.02% with rotary inertia. Cut-out plates are validated with results obtained using the finite element method, and the max variation observed between established results and present formulation is 1.3%. Establishing the accuracy of the current formulation, new results are obtained for rectangular cut-out plates resting on an elastic foundation of various stiffness parameters. The effect of incrementing cut-out dimensions and different layouts of cut-outs in the plate on the free vibration response of plates resting on an elastic foundation is investigated, along with the effects of varying aspect ratios and thickness-to-side ratios.