Nonlinear vibration analysis of FGM sandwich structure under thermal loadings

Abstract

The geometrically nonlinear thermal frequencies of the functionally graded (FG) sandwich structures are predicted numerically in the current work considering the variable temperature distributions (linear and nonlinear). For numerical analysis of the FG sandwich structure, an in-house finite element code has been developed in MATLAB using the higher-order shear deformation theory (HSDT) and Green–Lagrange nonlinear strain kinematics. The governing equation of motion for the graded sandwich structure is obtained using Hamilton’s principles, and the direct iterative method is used to predict the nonlinear vibration response of the sandwich structure. The temperature distributions along the thickness of the sandwich structure are considered. Temperature dependent material properties are considered in the present work for computation of frequency responses under thermal environment. The material properties are described in accordance with the power-law distribution. The current models are initially validated with the published results. The influence of various input parameters, i.e. the curvature ratio (CRO), thickness ratio (TRO), aspect ratio (ARO), boundary conditions, and power-law indices on the nonlinear vibration behaviours of FG sandwich structure have been studied.