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

Abstract

Abstract 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.