Vibration analysis of non-homogenous single-link flexible manipulator in uncertain environment

Abstract

This paper presents a novel dynamic model of a dual-cable-strapped single-link flexible manipulator under an uncertain workspace. The material of the link of the manipulator is considered to be non-homogeneous with inherent non-linearity, which is crucial in modelling. In this regard, linear and quadratic variations in the density of the material of the flexible link with space coordinates are considered. Uncertainty is introduced into its parameters in order to make the real-time dynamics of the flexible manipulator more challenging. Fuzzy parameters, in support of uncertainty, are invoked in the spring constants of the cables for modelling using Triangular Fuzzy Numbers (TFN). In particular, Interval Type-2 Triangular Fuzzy Numbers (IT2TFN) are considered in this investigation since higher-order fuzzy numbers can be beneficial, as the presence of uncertainty in the membership grade may also be unavoidable. The non-homogeneous flexible link is modelled as an Euler-Bernoulli beam, and the non-linear equations of motion are derived using Hamilton's principle and two boundary conditions. It may be difficult to obtain the exact solution of the governing differential equation because of the non-homogeneity in the parameters associated with the link. In this regard, the Adomian Decomposition Method (ADM) is implemented in the crisp as well as uncertain scenario to determine the natural frequencies of the single-link flexible manipulator. The existence and uniqueness of the solution is also illustrated. Tabular and graphical results are presented for validation and better visualisation.