A nonlinear viscoelastic damper is designed for several industrial applications. The damper is structurally similar to typical commercial dampers and the design is based on the choice of the viscoelastic material used as damping agent in the damper. Given the rheological parameters of certain material known from experiments, the coefficients of Johnson-Segalman constitutive equation model for the material are evaluated by fitting the data. The problem is first formulated by writing the governing equations for the flow between two parallel flat plates, i.e. Couette flow. The velocity and stress are represented by symmetric and antisymmetric Chandrasekhar functions in space. Both inertia and normal stress effects are included. A numerical scheme is applied to solve the governing equations in time domain projected by Galerkin method. For given Reynolds number and viscosity ratio, two critical Weissenberg numbers are found at which an exchange of stability occurs between the Couette and other steady flows. The model is capable of predicting the nonlinear amplitude-dependent behavior of viscoelastic dampers under single and multiple-frequency excitations.

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