Time- and frequency-domain linear viscoelastic modeling of highly damped aerospace structures

The numerical modeling of highly damped viscoelastic materials is critical for aerospace applications such as dynamic analysis of solid rocket motors - showing high damping ratios due to the presence of solid propellant - and design of passive damping devices for minimizing vibrations in aeronautical and space systems. Time-domain viscous damping models - giving damping forces proportional to velocities - are directly applicable in transient simulations, but they give a frequency-linear dissipative behavior which has no experimental evidence. On the other hand, frequency-domain hysteretic damping models - giving damping forces proportional to displacements - result in a frequency-constant dissipation that better describes the behavior of certain materials. However, using such models in transient analyses may give unphysical, non-Hermitian and non-causal system response. This paper reviews a class of first-principle-based damping models commonly used in structural dynamics by deriving them as particular cases of a general continuum mechanics formulation. The proposed damping models are tuned, in their frequency-domain description, on material experimental data so providing a Hermitian and causal time-domain responses, and they are applied to highly damped, practical aerospace structures via Finite Element models. The proposed model is applied to two aerospace systems: a scaled-down test article dynamically representative of a solid rocket motor launch-vehicle stage and a two-dimensional airfoil with passive viscoelastic dampers for flutter suppression.