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This paper presents the theoretical analysis of a multilayered magneto-electro-thermoelastic hollow cylinder under unsteady and uniform surface heating.We obtain the exact solution of the transient thermal stress problem of the multilayered magneto-electro-thermoelastic hollow cylinder in the generalized plane strain state.As an illustration,we perform numerical calculations of a two-layered composite hollow cylinder made of piezoelectric and magnetostrictive materials and investigate the numerical results for displacement,stress,and electric and magnetic potential distributions in the transient state.Furthermore,the effects of the constraint condition in z direction are investigated by comparing the numerical results with that in the plane strain state.