The dynamic stability of a circularly tapered rotating beam subjected to a pulsating axial external excitation with thermal gradient was studied for all possible combinations of clamped, guided, pinned, fixed, and free boundary conditions. The equations of motion and associated boundary conditions were obtained using the extended Hamilton's principle. Then these equations of motion and the associated boundary conditions were non-dimensionalised. A set of Hill's equations were obtained from the

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... on-dimensional equations of motion by the application of the extended Galerkin method. The zones of parametric instability were obtained using Saito-Otomi conditions. The effects of various boundary conditions, thermal gradient, taper, and rotational speed on the regions of parametric instability were investigated and presented through a series of graphs. The results reveal that increasing rotational speed and taper have stabilizing effects, whereas increasing thermal gradient has a destabilizing effect for all boundary conditions of the beam.