OICC Press Journal of Solid Mechanics 2008-7683 7 1 2015 03 30 Free Vibration Analysis of Moderately Thick Functionally Graded Plates with Multiple Circular and Square Cutouts Using Finite Element Method 83 95 EN J Vimal Department of Mechanical Engineering, Motilal Nehru National Institute of Technology, Allahabad, India R.K Srivastava Department of Mechanical Engineering, Motilal Nehru National Institute of Technology, Allahabad, India A.D Bhatt Department of Mechanical Engineering, Motilal Nehru National Institute of Technology, Allahabad, India A.K Sharma Department of Mechanical Engineering, Madhav Institute of Technology & Science Gwalior, India Journal Article 2015 03 30 A simple formulation for studying the free vibration of shear-deformable functionally graded plates of different shapes with different cutouts using the finite element method is presented. The aim is to fill the void in the available literature with respect to the free vibration results of functionally graded plates of different shapes with different cutouts. The material properties of the plates are assumed to vary according to a power law distribution in terms of the volume fraction of the constituents. Validation of the formulation is done with the help of convergence studies with respect to the number of nodes and the results are compared with those from past investigations available only for simpler problems. In this paper rectangular, trapezoidal and circular plates with cutouts are studied and the effects of volume fraction index, thickness ratio and different external boundary conditions on the natural frequencies of plates are studied.