Hysteresis modelling and chaos prediction in one- and two-DOF hysteretic models. (English) Zbl 1179.74095
The paper presents a simulation of various hysteretic loops by means of additional state variables (internal ones). This modeling for energy dissipation allows to model accurately the loops of various forms reflecting, for example, the behavior of magnetorheological/electrorheological fluids in a damper/absorber as well as hysteresis in shape-memory alloys, and stress-strain hysteresis with transient process in a steel rope. The developed models are effective, enable the reproduction of minor loops, and show fast numerical convergence and a high degree of coincidence with test data. All these models are based on the Masing-Bouc-Wen’s structure. One-degree-of-freedom (one-DOF) hysteretic oscillations (highly nonlinear nonautonomous Masing and Bouc-Wen hysteretic models with discontinuous right-hand sides) are studied by using the earlier methodology. This methodology has been applied to predict stick-slip chaos in two-DOF discontinuous systems with friction and in other smooth and non-smooth systems. The algorithm proposed for quantifying regular and chaotic dynamics is simpler and faster from a computational point of view than standard procedures, and allows to trace regular/irregular responses of hysteretic systems. Then, the evolutions of chaotic regions and regions for pinched hysteresis in various control parameter planes are present as the amplitude of external excitations versus frequency and the amplitude of external excitation versus damper factor with increasing hysteretic dissipation. Chaotic regions are also found in the amplitude of external excitation versus hysteretic dissipation planes. These investigations allow to observe a wealth of hysteretic oscillator behavior and to demonstrate two important phenomena restraining and governing the occurrence of chaotic behavior as a function of hysteretic dissipation. Finally, the authors consider a two-DOF autonomous hysteretic system with friction. The conditions for occurrence of chaos in the system are found for autonomous coupled hysteretic oscillators under sliding friction in the plane of maximal static friction forces of both oscillators versus belt velocity. The corresponding examples of phase planes and hysteretic loops illustrate the obtained chaotic regimes.
Reviewer: I. A. Parinov (Rostov-na-Donu)
MSC:
| 74N30 | Problems involving hysteresis in solids |
| 70K55 | Transition to stochasticity (chaotic behavior) for nonlinear problems in mechanics |
| 37N15 | Dynamical systems in solid mechanics |
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