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AbstractThis paper investigates the free vibration of spinning stepped functionally graded material (FGM) circular cylindrical shells with general boundary conditions in a thermal environment. The artificial spring is implemented to simulate the general boundary constraints. Temperature-dependent material properties change constantly along the thickness direction. The Donnell-Mushtari shell theory is applied to derive the energy functions of thin stepped circular cylindrical shells, where the effect of centrifugal force and Coriolis force is taken into account. The modified Fourier-Ritz method is utilized to derive the frequency equations of the spinning stepped FGM circular cylindrical shells. The influences of spring stiffness, power-law index, and temperature on the traveling wave frequencies are investigated. The influence of configuration on the forward wave frequency and critical speed of three stepped shells, including the one-end thickened, the two-end thickened, and the middle-thickened stepped shells, is discussed. For each configuration, design strategies for the stepped shells are proposed. [ABSTRACT FROM AUTHOR]