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The axially moving belt is widely utilized in many industrial fields, such as civil, mechanical, electronic and vehicle engineering.Although the axially moving viscoelastic belt is the simple mechanical transmission device in engineering, it may reveal complicated dynamic behavior.The belt can be modeled as a string because its bending stiffness is relatively small and can be neglected.In the past two decades, the dynamic response of axially moving belt has received considerable attention from many researchers[1,2].and these studies are basically restricted to the in-plane oscillation.A few researchers have paid attention to the nonlinear transverse oscillations of an axially moving viscoelastic belt for the in-plane and out-of-plane[3].