MDoF mechanical systems with rate-independent hysteresis: Assessment of dimensionality, loop shapes, and mass ratio

We explore the dynamic behavior of Multi Degrees of Freedom (MDoF) mechanical systems characterized by rate-independent hysteretic properties. The study focuses on three main aspects: (i) the influence of system dimensionality; (ii) the combined effect of distinct hysteretic behaviors acting on different components, and (iii) the impact of mass ratio variations on the steady-state response. To this end, a general class of nonlinear hysteretic systems is defined using a non-dimensional formulation, and a Poincaré map-based continuation procedure is employed to numerically compute periodic solutions, determine their stability, and detect bifurcations. Moreover, the adoption of the Vaiana–Rosati model of hysteresis (VRM+D) enables a unified and thorough analysis of complex hysteretic loop shapes for the first time. The results obtained in a consistent set of case studies reveal how these internal features govern resonance phenomena, affect stability, mode interactions and lead to the occurrence of advanced bifurcation patterns, including quasi-periodic oscillations and chaos.