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.

KEYWORDS:

• Sinusoidal porosity model
• even and uneven porosity models
• material stochasticity
• first-order perturbation technique (FOPT)
• large amplitude vibration
• Von Karman
• finite element
• Monte Carlo simulation (MCS)

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) [grant number 2022R1F1A1069025]. This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education [grant number 2022R1A6A1A03056784].