A continuous piecewise internal friction model of hysteresis for use in dynamical simulations

The suitability of the internal friction models by Reid [Free vibration and hysteretic damping, Journal of the Royal Aeronautical Society 69 (1956) 283] and Muravskii [On frequency independent damping, Journal of Sound and Vibration 274 (2004) 653–668] for modelling hysteretic damping is investigated. Time-domain dynamical simulations of Reid's model reveal the presence of artefacts, which cause significant errors and solution stiffness in sub-resonant conditions. Muravskii's non-analytical modification of Reid's model is shown to be inconsistent with its primary goal of achieving continuity at the points of strain-rate reversal. An analytical constitutive equation for this model is derived and its implications discussed; the model is shown to be equivalent to Reid's model. Attempting to embody the original concept of Muravskii, a new variant of Reid's model is proposed, replacing the discontinuous sign function found in Reid and Muravskii with a continuous piecewise function. The new model is tested and compared to its predecessors for various steady state and transient oscillatory conditions, including resonance, and is found to be a competent alternative to the robust, but very frequency-sensitive, viscous model.