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This paper combines a self-adaptive precise algorithm in the time domain with the scaled boundary finite elementmethod(SBFEM)for solving viscoelastic problems with cyclic symmetry.By expanding variables at a discretized timeinterval,a coupled spatial-temporal problem can be decoupled into a series of recursive spatial problems which aresolved by SBFEM.It has been proved that the coefficient matrices of the global SBFEM equations for the cyclicallysymmetric system are block-circulant and both eigenproblem and stiffness matrix equation are partitioned into a series of independent sub-problems.In this way the computational efficiency is significantly increased by solving only aserious of sub-problems via a partitioning algorithm instead of solving the whole problem.Two numerical examples are given to illustrate the advantage of the proposed approach.