An iterated maps approach for dynamic ratchetting in sdof hysteretic damping systems

Dynamic ratchetting is a phenomenon in which plastic deformation increases in successive cycles. In the present paper, first, various characteristics of dynamic ratchetting are demonstrated based on numerical simulation. Second, iterated maps are developed as a tool for the investigation of dynamic ratchetting in a single degree of freedom (sdof) system. When an elasto-perfectly-plastic model is employed to represent hysteretic damping, a piecewise linear solution can be obtained and used to develop iterated maps. A stability investigation in the iterated maps shows that dynamic ratchetting is developed under a stable cycling. In this stable cycling, dynamic ratchetting occurs when an excitation function loses antiperiodicity (shift symmetry).