Saim,Ahmed2026-01-192026-01-192025-10-09https://dspace.univ-tlemcen.dz/handle/112/25585Cette étude présente une analyse numérique du comportement de tourbillonnement d’un arbre creux non uniforme en rotation, constitué de matériaux à gradient fonctionnel axial (FGM). The material properties vary continuously along the axial direction according to a power-law distribution. Using Timoshenko beam theory, the shaft is modeled with the pversion of the finite element method (FEM), while Lagrange’s formalism is applied to derive the differential equations governing the motion of the rotating system. The proposed model is used to analyze the system’s whirl frequencies, critical spinning speeds, and the influence of key parameters on the behavior and stability of dimensionless natural frequencies. These parameters include the slenderness ratio, material composition, radius variation, variable rotating speed, and power-law index, evaluated under various boundary conditions (B.C.). The effects of these factors performance of spinning hollow non-uniform shaft are understood. The validity of the proposed model is confirmed through comprehensive comparisons of numerical and analytical results with existing data in the literature. This work paves the way for innovative industrial applications in advanced rotating structures.enSpinning hollow shaftnon-uniform profileaxially FGMwhirling frequencyTimoshenko beam theoryThesis