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On the Hysteretic Bouc–Wen Model

Part I: Forced Limit Cycle Characterization

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Abstract

This paper deals with the problem of characterizing analytically the limit cycle of the Bouc–Wen model. This question arises often in parameter identification issues where the input is chosen to be periodic and the experimentally obtained limit cycle is then used to determine the model parameters. However, it has never been proved analytically that a T-periodic input leads to a T-periodic output for the Bouc–Wen model. Furthermore, an analytical expression of the limit cycle is lacking. The objective of this paper is to fill this gap by proving that the response of the Bouc–Wen model to a class of T-periodic inputs of practical interest in identification procedures is T-periodic. We also provide an exact explicit description of the limit cycle which will be used in the companion paper to derive an identification method for the Bouc–Wen model parameters.

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Authors and Affiliations

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

    Fayçal Ikhouane & José Rodellar

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  1. Fayçal Ikhouane
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  2. José Rodellar
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Correspondence to Fayçal Ikhouane.

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Contributed by Prof. F. Casciati.

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Ikhouane, F., Rodellar, J. On the Hysteretic Bouc–Wen Model. Nonlinear Dyn 42, 63–78 (2005). https://doi.org/10.1007/s11071-005-0069-3

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  • DOI: https://doi.org/10.1007/s11071-005-0069-3

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