Ikhouane, Fayçal; Hurtado, Jorge E.; Rodellar, José Variation of the hysteresis loop with the Bouc-Wen model parameters. (English) Zbl 1180.70029 Nonlinear Dyn. 48, No. 4, 361-380 (2007). Summary: 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. Cited in 7 Documents MSC: 70K05 Phase plane analysis, limit cycles for nonlinear problems in mechanics 34C55 Hysteresis for ordinary differential equations 74C05 Small-strain, rate-independent theories of plasticity (including rigid-plastic and elasto-plastic materials) Keywords:Bouc-Wen model; Hysteresis; Parameters; Hysteresis loop PDFBibTeX XMLCite \textit{F. Ikhouane} et al., Nonlinear Dyn. 48, No. 4, 361--380 (2007; Zbl 1180.70029) Full Text: DOI References: [1] Bouc, R.: Forced vibrations of mechanical systems with hysteresis. In: Proceedings of the Fourth Conference on NonLinear Oscillations, Prage, (1967) [2] Baber, T.T., Wen, Y.K.: Stochastic equivalent linearization for hysteretic degrading multistory structures. 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