A hysteretic model of localized frictional contacts with instrumental stiffness

The steady-state dynamic response of a single-degree-of-freedom system comprising both a hysteretic element and a spring is considered. The Hertz–Cattaneo–Mindlin theoretical framework for modeling of local tangential contact with friction is applied in conjunction with the Masing model of hysteresis to describe the hysteretic behavior of the multiple localized frictional contact interface. The steady-state tangential displacement amplitude of a rigid body under harmonic tangential force excitation is approximately determined by means of the equivalent linearization technique, based on the harmonic balance principle. A special attention is paid to the evaluation of the frictional damping and the determination of the backbone curve of the Masing model from the dissipation-amplitude relation.