Vibration response of functionally graded material sandwich plates with elliptical cutouts and geometric imperfections under the mixed boundary conditions

Abstract

Abstract The present article investigates the effect of elliptical cutouts and geometric imperfections on the vibrational response of functionally graded material (FGM) sandwich plates. Generalised governing equations for the sandwich FGM (SFGM) plate are derived based on non-polynomial higher-order shear deformation theory. Geometric discontinuities have been incorporated as elliptical cutouts in the plates, and the various geometric imperfections are modelled using the generic function. The mathematical modelling has been carried out using the C0 continuity isoparametric finite element formulation by considering four-noded elements with seven degrees of freedoms per node. Convergence and validation studies have been performed to demonstrate the efficiency and accuracy of the present methodology. The influence of volume fraction index, geometric imperfections, and elliptical cutouts on the vibrational frequency of SFGM plates have been analysed under the mixed boundary conditions.