The uncertain free vibration analysis of functionally graded sandwich plates placed on a variable elastic foundation

Abstract This study presents an enhanced finite element method (FEM) integrated with the improved first-order shear deformation theory (i-FSDT) for analyzing the natural frequencies of functionally graded sandwich (FGSW) plates resting on a variable elastic foundation (VEF) with uncertain input parameters. The FGSW plates are composed of two functionally graded (FG) face layers and a homogeneous or FG core layer. The proposed method is validated by comparing it with existing benchmark solutions to ensure its accuracy and reliability. In addition, the study explores the effects of geometric configurations, material properties, foundation types, and boundary conditions (BCs) on the natural frequencies of FGSW plates. To address uncertainty in input parameters, Monte Carlo simulation (MCS) is employed to determine the probabilistic range of natural frequencies. The numerical and graphical results show that the uncertainties of the input parameters interact to greatly affect the natural frequency of sandwich plates.