Hysteresis modelling and chaos prediction in one- and two-DOF hysteretic models
type: Item
instance of: scholarly article
title: Hysteresis modelling and chaos prediction in one- and two-DOF hysteretic models
zbMATH Open document ID: 1179.74095
author: Larisa Dzyubak
author: Jan Awrejcewicz
published in: Archive of Applied Mechanics
publication date: 2007-05-04T00:00:00Z
review text: 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 foun…
Mathematics Subject Classification ID: 74N30
Mathematics Subject Classification ID: 70K55
Mathematics Subject Classification ID: 37N15
zbMATH DE Number: 5149263
zbMATH Keywords: parametric space
zbMATH Keywords: Masing-Bouc-Wen's structure
zbMATH Keywords: hysteretic dissipation
zbMATH Keywords: friction
reviewed by: Ivan A. Parinov
MaRDI profile type: Publication
full work available at URL: s00419-006-0101-1
OpenAlex ID: W2043973324
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DOI: 10.1007/S00419-006-0101-1
description: scientific article; zbMATH DE number 5149263