Rheological modeling of viscoelastic passive dampers

An efficient method of modeling the rheological behavior of viscoelastic dampers is discussed and illustrated. The method uses the standard mechanical model composed of linear springs and dashpots, which leads to a Prony series representation of the corresponding material function in the time domain. The computational procedure used is simple and straightforward and allows the linear viscoelastic material functions to be readily determined from experimental data in the time or frequency domain. Some existing models including the fractional derivative model and modified power-law are reviewed and compared with the standard mechanical model. It is found the generalized Maxwell and generalized Voigt model accurately describe the broadband rheological behavior of viscoelastic dampers commonly used in structural and vibration control. While a cumbersome nonlinear fitting technique is required for other models, a simple collocation or least-squares method can be used to fit the standard mechanical model to experimental data. The remarkable computational efficiency associated with the exponential basis functions of the Prony series greatly facilitates fitting of the model and interconversion between linear viscoelastic material functions. A numerical example on a viscoelastic fluid damper demonstrates the advantages of the use of the standard mechanical model over other existing models. Details of the computational procedures for fitting and inter-conversion are discussed and illustrated.