Dynamic ratchetting in hysteretic damping systems
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In the present study, dynamic ratchetting of hysteretic damping systems is investigated via numerical simulations and analytical approximations. Ratchetting in the field of material plasticity is defined as continuous increments of the plastic deformation with cycling under quasi-static loading conditions. It is shown herein that ratchetting behavior can also be developed under dynamic loading conditions. This behavior is called dynamic ratchetting in the present study. Three plasticity models are considered in describing hysteretic damping: the elasto-perfectly-plastic model, the linear kinematic hardening model, and the two-surface model. Under multi-frequency sinusoidal excitations, dynamic ratchetting occurs in the elasto-perfectly-plastic model and the two-surface model when the ratio between frequencies is an integer number (commensurable), and the product of terms comprising the ratio is an even number. Otherwise, dynamic ratchetting is not developed. Under incommensurable frequency excitations, motions are quasi-periodic and dynamic ratchetting does not occur. Dynamic ratchetting can be found in Single Degree-Of-Freedom, Two Degrees-Of-Freedom, and N-Degrees Of Freedom dynamic systems. A piecewise linear approach is adopted to obtain the analytical approximation of SDOF dynamic motion with the elasto-perfectly-plastic model under commensurable frequency sinusoidal excitations. Based on the one-dimensional iterated map functions, the stability of dynamic motion can be characterized following concepts from nonlinear dynamic studies. The existence of stable cycling of TDOF and N-DOF systems is investigated by the proposed state based approach. With the existence of a stable cycling, dynamic ratchetting effects are represented by the change of plastic deformation within a cycle. If the deformation change is not equal to zero, then the deformation increases in successive cycles, which corresponds to dynamic ratchetting. In order to investigate possible dynamic ratchetting under earthquake excitations, the frequency contents of selected earthquake strong motions are investigated utilizing spectrograms. Spectrograms show that some earthquakes contain long enough durations of multifrequency excitations that can develop dynamic ratchetting. Under those strong motions, SDOF systems and a 10-story shear building are shown to dynamic ratchetting.