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

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Abstract

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.

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Authors and Affiliations

  1. Departament de Matemàtica Aplicada III, Universitat Politècnica de Catalunya, Escola Universitària d’Enginyeria Tècnica Industrial de Barcelona, 187 Comte d’Urgell, 08036, Barcelona, Spain

    Fayçal Ikhouane

  2. Universidad Nacional de Colombia, Apartado 127, Manizales, Colombia, USA

    Jorge E. Hurtado

  3. Departament de Matemàtica Aplicada III, Universitat Politècnica de Catalunya, Jordi Girona 1-3, 08034, Barcelona, Spain

    José Rodellar

Authors
  1. Fayçal Ikhouane
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  2. Jorge E. Hurtado
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  3. José Rodellar
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Correspondence to Fayçal Ikhouane.

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Ikhouane, F., Hurtado, J.E. & Rodellar, J. Variation of the hysteresis loop with the Bouc–Wen model parameters. Nonlinear Dyn 48, 361–380 (2007). https://doi.org/10.1007/s11071-006-9091-3

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  • DOI: https://doi.org/10.1007/s11071-006-9091-3

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