Estimation of the dynamical properties of polyurethane foam through use of Prony series

A system identification procedure is formulated for estimation of parameters associated with a dynamic model of a single-degree-of-freedom foam-mass system. The foam is modelled as a linear viscoelastic material, whose constitutive law is expressed by an exponential hereditary relaxation kernel. The identification procedure is based on modelling the free response of the system as a Prony series (sum of exponentials terms) and fitting this Prony series to the data. This estimated response model is then utilized to estimate the parameters in the system model based on an explicit solution of the model. The procedure is analyzed for its reliability under different sources of error and uncertainties, such as the presence of weak components and experimental noise, and some modifications are evaluated to improve the robustness of the procedure. Finally, the procedure is applied to experimental data to obtain relevant stiffness, viscous and viscoelastic parameters associated with the system. Variations in values of these parameters as a function of static compression are also investigated.