In this paper, the non-linear dynamic stability of viscoelastic transmission belt with time dependent velocities is investigated. Based on the constitutive description of Kelvin viscoelastic material and the motion equation of the axially moving belt, the nonlinear dynamic model that dominates the transverse vibration of the viscoelastic transmission belt is established.Then the non linear dynamic stability is studied by using multiple scale method. It is found that: 1) for fluctuation frequency away from zero or two times the natural frequency, the amplitudes of vibration are bounded and the phases are the logarithm functions in time. The non-linear effects become important for velocities close to critical velocity. 2) for fluctuation frequencies close to zero, the amplitudes of vibration are bounded. 3) for fluctuation frequencies close to two times the natural frequency, two non-trivial solutions bifurcate from the trivial steady-state solution. There are two supercritical pitchfork bifurcation points. Passing through the first bifurcation point, the trivial solution looses stability and a non-trivial solution is obtained.If frequency is increased and pass through the second bifurcation point, the trivial solution is again stale and non trivial solutions disappear.
