Free vibration analysis of the geometrically nonlinear functionally graded porous curved panels in deterministic and stochastic domains considering various boundary conditions

Abstract

This study focuses on the analysis of free vibrations in functionally graded (FG) panels with characteristics such as porosity, curvature, and geometric nonlinearity. The analysis encompasses both deterministic and stochastic domains while considering a range of boundary conditions. The nonlinear finite element formulation adopted in this study is based on a higher-order nonlinear shell theory that incorporates the von Karman geometric nonlinearity. The material properties of the FG curved panels are graded using a power law distribution. The investigation includes four different boundary conditions and various types of curved panels, namely spherical, hyperbolic paraboloidal, elliptical, and cylindrical. Stochastic analysis employs the first-order perturbation technique (FOPT), while Monte Carlo simulation (MCS) is employed solely for validating the FOPT model. The study explores the influence of boundary conditions, panel types, porosity distribution, volume fraction index, and other factors in both deterministic and stochastic domains, taking into account randomness in material properties. The stochasticity in the geometric properties like dimensions, and boundary conditions can be the potential future scope of this study.