Models of viscoelasticity with complex-order derivatives

In this paper it is shown that the order of time derivative and the coefficients in linear viscoelastic models can be generalized to complex quantities. In this approach, the storage and loss moduli are not regarded as two independent real functions but rather as the real and imaginary parts of a complex function. The problem of calibration of models with complex parameters is solved by resorting to methods of nonlinear regression in the complex space. The conditions for existence of complex-order time derivatives are examined and the transformation of these derivatives in the frequency domain is derived. The procedure is applied in the development of models for viscous dampers. The models are shown to produce results in good agreement with experimental data.