The propagation of uncertainty in the geometrically nonlinear responses of smart sandwich porous cylindrical shells reinforced with graphene platelets

Abstract

This paper is concerned with the analysis of uncertainty propagation in the nonlinear dynamic responses of smart sandwich cylindrical shells under rectangular, sine, and exponential loads. The sandwich shells are composed of a functionally graded porous (FGP) core reinforced with nanocomposite graphene platelets (GPLs) and surrounded by two piezoelectric layers. Various sources of uncertainties related to the material properties, the geometry of the reinforcements, and piezoelectric parameters are considered in this study. The uncertainty propagations in the nonlinear dynamic responses of the shells are examined for different variations of GPL dispersions and porosity distributions in the core. For this purpose, three different distributions for porosity and three different dispersions for graphene platelets have been considered in the thickness direction. In order to investigate the uncertainty propagation in the responses of the shells, the interval analysis method which is an appropriate technique for the uncertainty analysis of systems with bounded uncertainties is utilized. The Halpin-Tsai model is used to find the effective properties of the GPL-reinforced materials. The equations of motion are derived based on the higher-order shear deformation theory and Sanders’ nonlinear theory. In order to solve the equations of motion and to obtain the dynamic responses of the shells, the Fourier differential quadrature (FDQ) technique is employed. According to the analysis results, the sensitivities of the responses of internal moment, displacement, and internal force have the highest values relative to the uncertainty sources, respectively, whereas the uncertainty percentages for the responses of displacement, internal moment, and internal force respectively have the highest values for the examined loads.