A study of the natural frequencies of the functionally graded curved beams including porosities: Deterministic and stochastic modeling

Abstract

In this research article, an investigation into the natural frequencies of functionally graded porous curved beams is presented, covering both deterministic and stochastic domains. The stochastic finite element analysis is based on a three-node, C0 continuous element, and higher-order shear deformation theory, utilizing the first-order perturbation technique (FOPT). The study includes a comparative analysis of three porosity distribution models, including a recently proposed sinusoidal model. Additionally, the study examines the influence of various factors, such as porosity distributions, boundary conditions, volume fraction indices, and geometric configurations, on the natural frequencies. The analysis encompasses uncertain natural frequencies in functionally graded curved beams, accounting for material stochasticity through FOPT. Monte Carlo simulation (MCS) is used to validate the accuracy of the FOPT model, increasing the approach’s reliability. Potential future research in this area could investigate the effects of stochastic variations in geometric parameters, including dimensions and boundary conditions.