Hysteretic Systems: Resonances, Modal Coupling, Mitigation

Several mechanical systems are characterized by hysteresis The Bouc-Wen model, simple but effective, has been adopted. First, the response of a hysteretic oscillator is illustrated by frequency response curves. The response depends on the oscillation amplitude: the resonance peak moves left with the increasing amplitude, according to the hysteresis softening nonlinearity. Then, the phenomena of nonlinear modal coupling are investigated by means of a two degree-of-freedom system. For increasing excitation system frequencies change and in turn their ratio changes; so, internal resonance conditions easily occur, with evident interaction phenomena. For a critical excitation intensity, the branch of resonance solutions of the first mode experiences a bifurcation and a novel mode arises. The occurrence of this superabundant mode is characterized by a notable transfer of energy between the two modes, with beneficial vibration mitigation. A case study of a barrier structure excited by the passage of high-speed trains is investigated, showing the performance of an added hysteretic device, which makes the energy transfer between the two modes easier.