Dynamic Analysis of Generalized Viscoelastic Fluids

A general boundary‐element formulation is presented for the prediction of the dynamic response of fluids with viscoelastic behavior. The fluid is modeled by a generalized constitutive relation that contains either complex‐valued parameters and complex‐order derivatives or real‐valued parameters and fractional‐order derivatives. These models are consistent with basic theories and are not arbitrary constructions. The models are valid for linear viscoelastic fluid behavior and are limited to fluid motions with infinitesimally small displacement gradients. The governing equations are transformed into the Laplace domain and the infinite space fundamental solution is derived. The resulting integral equations are then solved by numerical procedures. The method is applied in the prediction of the dynamic mechanical properties of a viscous damper containing a viscoelastic fluid in the form of silicon gel. The fluid is modeled by a fractional derivative Maxwell model. The predicted mechanical properties of the device are found to be in excellent agreement with experimental results.