Structural systems often show nonlinear behavior under severe excitations generated by natural hazards. In that condition, the restoring force becomes highly nonlinear showing significant hysteresis. The hereditary nature of this nonlinear restoring force indicates that the force cannot be described as a function of the instantaneous displacement and velocity. Accordingly, many hysteretic restoring force models were developed to include the time dependent nature using a set of differential equations. This survey contains a review of the past, recent developments and implementations of the Bouc-Wen model which is used extensively in modeling the hysteresis phenomenon in the dynamically excited nonlinear structures.

The Hysteresis Bouc-Wen Model, a Survey

A mathematical model of the factional behavior of Teflon sliding bearings for conditions of interest in base isolation is developed. The calibration of the model is based on extensive experimental data that were presented in an accompanying paper. The model is capable of accounting for: (1) Unidirectional and multidirectional motion at the Teflon‐steel interface; (2) velocity and pressure dependence of the coefficient of sliding friction; and (3) breakaway (or static) friction effects. The model is characterized by four parameters. These are the minimum and maximum values of the sliding coefficient of friction, the ratio of breakaway to sliding coefficient of friction at initiation of sliding and a parameter that describes the variation of the sliding coefficient of friction with velocity. Values of these parameters are presented for sixteen combinations of type of Teflon, bearing pressure and condition (surface roughness) of mating steel surface. Applications of the model in the analysis/design of a slid...

Teflon Bearings in Base Isolation II: Modeling

Preface. List of Figures. List of Tables. 1. Introduction 1.1 Objective and contents of the book 1.2 The Bouc-Wen model: origin and literature review 2. Physical consistency of the Bouc-Wen model 2.1 Introduction 2.2 BIBO stability of the Bouc-Wen model 2.2.1 The model 2.2.2 Problem statement 2.2.3 Classi ~ cation of the BIBO stable Bouc-Wen models 2.2.4 Practical remarks 2.3 Free motion of a hysteretic structural system 2.3.1 Problem statement 2.3.2 Asymptotic trajectories 2.3.3 Practical remarks 2.4 Passivity of the Bouc-Wen model 2.5 Limit cases 2.5.1 The limit case n = 1 2.5.2 The limit case (r) = 1 2.5.3 The limit case (r) = 0 2.5.4 The limit case ~ + - = 0 2.6 Conclusion 3 Forced limit cycle characterization of the Bouc-Wen model 3.1 Introduction 3.2 Problem statement 3.2.1 The class of inputs 3.2.2 Problem statement 3.3 The normalized Bouc-Wen model 3.4 Instrumental functions 3.5 Characterization of the asymptotic behavior of the hysteretic output 3.5.1 Technical Lemmas 3.5.2 Analytic description of the forced limit cycles for the Bouc-Wen model 3.6 Simulation example 3.7 Conclusion 4 Variation of the hysteresis loop with the Bouc-Wen model parameters 4.1 Introduction 4.2 Background results and methodology of the analysis 4.2.1 Background results 4.2.2 Methodology of the analysis 4.3 Maximal value of the hysteretic output 4.3.1 Variation with respect to 4.3.2 Variation with respect to 4.3.3 Variation with respect to n 4.3.4 Summary of the obtained results 4.4 Variation of the zero of the hysteretic output 4.4.1 Variation with respect to 4.4.2 Variation with respect to 4.4.3 Variation with respect to n 4.4.4 Summary of the obtained results 4.5 Variation of the hysteretic output with the Bouc-Wen model parameters 4.5.1 Variation with respect to 4.5.2 Variation with respect to 4.5.3 Variation with respect to n 4.5.4 Summary of the obtained results 4.6 The four regions of the Bouc-Wen model 4.6.1 The linear region Rl 4.6.2 The plastic region Rp 4.6.3 The transition regions Rt and Rs 4.7 Interpretation of the normalized Bouc-Wen model parameters 4.7.1 The parameters and 4.7.2 The parameter 4.7.3 The parameter n 4.8 Conclusion 5 Robust identification of the Bouc-Wen model parameters 5.1 Introduction 5.2 Parameter identi ~ cation for the Bouc-Wen model 5.2.1 Class of inputs 5.2.2 Identi ~ cation methodology 5.2.3 Robustness of the identi ~ cation method 5.2.4 Numerical simulation example 5.3 Modeling and identi ~ cation of a magnetorheological damper 5.3.1 Some insights into the viscous + Bouc-Wen model for shear mode MR dampers 5.3.2 Alternatives to the viscous + Bouc-Wen model for shear mode MR dampers 5.4 Identi ~ cation methodology for the viscous + Dahl model . . 5.4.1 Numerical simulations 5.5 Conclusion 6 Control of a system with a Bouc-Wen hysteresis 6.1 Introduction and problem statement 6.2 Control design and stability analysis 6.3 Numerical simulation 6.4 Conclusion A Mathematical background A.1 Existence and uniqueness of solutions A.2 Concepts of stability A.3 Passivity and absolute stability A.3.1 Passivity in mechanical systems A.3.2 Positive realness A.3.3 Sector functions A.3.4 Absolute stability A.4 Input-output properties References. Index.

Systems with Hysteresis: Analysis, Identification and Control Using the Bouc-Wen Model

This paper presents the benchmark problem definition for seismically excited base-isolated buildings. The objective of this benchmark study is to provide a well-defined base-isolated building with a broad set of carefully chosen parameter sets, performance measures and guidelines to the participants, so that they can evaluate their control algorithms. The control algorithms may be passive, active or semi-active. The benchmark structure considered is an eight-storey base-isolated building similar to existing buildings in Los Angeles, California. The base isolation system includes both linear and nonlinear bearings and control devices. The superstructure is considered to be a linear elastic system with lateral–torsional behavior. A new nonlinear dynamic analysis program has been developed and made available to facilitate direct comparison of results of different control algorithms. Copyright © 2005 John Wiley & Sons, Ltd.

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Smart base‐isolated benchmark building. Part I: problem definition

In base‐isolated structures specially designed isolation systems provide the needed flexibility and energy dissipation capacity. The isolation systems, which can be either elastomeric or sliding systems, exhibit highly nonlinear behavior. The existing algorithms cannot analyze base‐isolated structures with sliding isolation systems accurately. This paper presents an analytical model and a solution algorithm developed for nonlinear dynamic analysis of three‐dimensional‐base‐isolated structures with elastomeric and/or sliding isolation systems. The novelty of the analytical model and solution algorithm is its capability to capture the highly nonlinear frictional behavior of sliding isolation systems in plane motion. Nonlinear behavior is restricted to the base and the superstructure is considered to be elastic at all times. Biaxial and uniaxial models, which can represent both elastomeric and sliding isolation bearings, are presented. The solution algorithm consisting of the pseudoforce method with iteratio...

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Nonlinear Dynamic Analysis of 3‐D‐Base‐Isolated Structures

A random vibration method is developed for the response analysis of hysteretic structural systems under stochastic two-dimensional earthquake excitations. The biaxial hysteretic restoring force is modelled by coupled non-linear differential equations; the response statistics are obtained using the equivalent linearization technique. The validity of the proposed model is appraised using available biaxial loading tests of reinforced concrete columns. A parametric study was performed to examine the significance of the effects of biaxial interaction under earthquake excitations. A practical method to evaluate the extreme response statistics is also presented.

Y. J. Park

Papers

Random vibration of hysteretic systems under bi-directional ground motions