Variation of the hysteresis loop with the Bouc–Wen model parameters

The Bouc–Wen model for smooth hysteresis has received an increasing interest in the last few years due to the ease of its numerical implementation and its ability to represent a wide range of hysteresis loop shapes. This model consists of a first-order nonlinear differential equation that contains some parameters that can be chosen, using identification procedures, to approximate the behavior of given physical hysteretic system. Despite a large body of literature dedicated to the Bouc–Wen model, the relationship between the parameters that appear in the differential equation and the shape of the obtained hysteresis loop is little understood. The objective of this paper is to fill this gap by analytically exploring this relationship using a new form of the model called the normalized one. The mathematical framework introduced in this study formalizes the vague notion of “loop shape" into precise quantities whose variation with the Bouc–Wen model parameters is analyzed. In light of this analysis, the parameters of Bouc–Wen model are re-interpreted.

[1]  Y. Wen.  Method for Random Vibration of Hysteretic Systems , 1976 .

[2]  Y. K. Wen,et al.  Stochastic Seismic Performance Evaluation of Buildings , 1983 .

[3]  Y. K. Wen,et al.  Stochastic Analysis of Liquefaction Under Earthquake Loading , 1983 .

[4]  S. T. Mau,et al.  Systems Identification of Degrading Hysteretic Restoring Forces , 1988 .

[5]  Fabio Casciati,et al.  Stochastic dynamics of hysteretic media , 1989 .

[6]  S. Lau,et al.  Steady-state oscillation of hysteretic differential model. I: Response analysis , 1994 .

[7]  Greg Foliente,et al.  Hysteresis Modeling of Wood Joints and Structural Systems , 1995 .

[8]  T. Low,et al.  Modeling of a three-layer piezoelectric bimorph beam with hysteresis , 1995 .

[9]  Shirley J. Dyke,et al.  PHENOMENOLOGICAL MODEL FOR MAGNETORHEOLOGICAL DAMPERS , 1997 .

[10]  Yi-Qing Ni,et al.  IDENTIFICATION OF NON-LINEAR HYSTERETIC ISOLATORS FROM PERIODIC VIBRATION TESTS , 1998 .

[11]  Satish Nagarajaiah,et al.  Response of Base-Isolated USC Hospital Building in Northridge Earthquake , 2000 .

[12]  Billie F. Spencer,et al.  “Smart” Base Isolation Strategies Employing Magnetorheological Dampers , 2002 .

[13]  Elias B. Kosmatopoulos,et al.  Development of adaptive modeling techniques for non-linear hysteretic systems , 2002 .

[14]  J. Rodellar,et al.  Bounded and dissipative solutions of the Bouc-Wen model for hysteretic structural systems , 2004, Proceedings of the 2004 American Control Conference.

[15]  Silvano Erlicher,et al.  Thermodynamic admissibility of Bouc-Wen type hysteresis models , 2004 .

[16]  H. Zhang,et al.  Parameter Analysis of the Differential Model of Hysteresis , 2004 .

[17]  F. Ikhouane,et al.  On the Hysteretic Bouc–Wen Model , 2005 .

[18]  Sergio M. Savaresi,et al.  Identification of semi-physical and black-box non-linear models: the case of MR-dampers for vehicles control , 2005, Autom..