Dynamic Analysis of Cracked Functionally Graded Single-Link Manipulator under Fuzzy Environment using Higher-Order Shear Deformation Theory

In this paper, the free vibration analysis of a functionally graded single-link manipulator (FGSLM) with a crack is investigated. The study employs higher-order shear deformation theory (HSDT), providing a more accurate depiction of the link's behaviour by considering shear effects, significant deformations, and higher-order bending dynamics. The density of the link (ρ) varies in the thickness direction according to a power law function. Additionally, uncertainty is introduced into the parameters of the flexible manipulator to enhance its real-time dynamics. Fuzzy parameters are employed in the density of two different types of materials in functionally graded compositions to account for uncertainty. This study emphasises Triangular Fuzzy Numbers (TFN) because of their effectiveness in managing parameter ambiguity that cannot be eliminated. The governing differential equation has been solved analytically, and natural frequencies have been obtained. Existing results with Timoshenko beam theory (TBT) are compared with new results obtained with HSDT for validation. Frequencies under an uncertain environment have been computed with material uncertainty for different cases of uncertainty.