A general boundary-element formulation is presented for the prediction of the dynamic response of systems consisting of materials that behave viscoelastically with mechanical properties that depend strongly on both frequency and temperature. The developed formulation accounts for any linear viscoelastic incompressible material, where the constitutive law can contain fractional- or complex-order derivatives. The method of reduced variables is introduced to construct the master curves of the dynamic modulus of the fluid at some reference temperature, from experimental data at different temperatures. Three generalized-derivative (fractional and complex order) constitutive models are proposed to approximate the dynamic modulus of viscoelastic fluids over a large frequency range. The complex parameters of the proposed models are then obtained by best fitting of the master curves. The solution of the problem is obtained by transforming the constitutive and balance equations in the Laplace domain. The method is applied in the prediction of the mechanical properties of a damper containing such a viscoelastic fluid. The numerical predictions of the developed boundary element method using the proposed generalized-derivative constitutive models are compared against experimental data.

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