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

General features of the hysteretic behavior of wood joints and structural systems are characterized, and the available hysteresis models for wood systems are reviewed. A general hysteresis model for single- and multiple-degree-of-freedom wood joints and structural systems, based on a modification of the Bouc-Wen-Baber-Noori model, is presented and used in nonlinear dynamic analysis of single-degree-of-freedom wood systems. The hysteretic constitutive law produces a smoothly varying hysteresis that models previously observed behavior of wood joints and structural systems, such as nonlinearity, strength and stiffness degradation, and pinching. It takes into account the experimentally observed dependence of wood joints' response to the input and response at an earlier time (known as memory). Hysteresis shapes produced by the model are shown to compare favorably with experimental hysteresis of wood joints with (1) yielding plates; (2) yielding nails; and (3) yielding bolts.

/pdf/hysteresis-modeling-of-wood-joints-and-structural-systems-25nuheyxe0.pdf

Hysteresis Modeling of Wood Joints and Structural Systems

The extended Bouc-Wen differential model is one of the most widely accepted phenomenological models of hysteresis in mechanics. It is routinely used in the characterization of nonlinear damping and in system identification. In this paper, the differential model of hysteresis is carefully re-examined and two significant issues are uncovered. First, it is found that the unspecified parameters of the model are functionally redundant. One of the parameters can be eliminated through suitable transformations in the parameter space. Second, local and global sensitivity analyses are conducted to assess the relative sensitivity of each model parameter. Through extensive Monte Carlo simulations, it is found that some parameters of the hysteretic model are rather insensitive. If the values of these insensitive parameters are fixed, a greatly simplified model is obtained.

Parameter Analysis of the Differential Model of Hysteresis

The generalized model of differential hysteresis contains 13 control parameters with which it can curvefit practically any hysteretic trace. Three identification algorithms are developed to estimate the control parameters of hysteresis for different classes of inelastic structures. These algorithms are based upon the simplex, extended Kalman filter, and generalized reduced gradient methods. Novel techniques such as global search and internal constraints are incorporated to facilitate convergence and stability. Effectiveness of the devised algorithms is demonstrated through simulations of two inelastic systems with both pinching and degradation characteristics in their hysteretic traces. Owing to very modest computing requirements, these identification algorithms may become acceptable as a design tool for mapping the hysteretic traces of inelastic structures.

Parameter identification of inelastic structures under dynamic loads

Many civil and mechanical structures exhibit hysteresis with degradation and/or pinching when subject to severe cyclic loadings such as earthquakes, wind, or sea waves. The modeling and identification of non-linear hysteretic systems with degradation and pinching is therefore a practical problem encountered in the engineering mechanics field. On-line identification of degrading and pinching hysteretic systems is quite a challenging problem because of its complexity. A recently developed technique, the unscented Kalman filter (UKF) which is capable of handling any functional non-linearity, is applied to the on-line parametric system identification of hysteretic differential models with degradation and pinching. Simulation results show that the UKF is efficient and effective for the real-time state estimation and parameter identification of highly non-linear hysteretic systems with degradation and pinching.

Real-time parameter estimation for degrading and pinching hysteretic models

A simple constructive technique for the development of rate-type hysteresis models for general nonlinear system is presented. The technique is used to develop hysteresis models to incorporate time history-dependent postyield restorting forces, and general pinching behavior in smoothly varying deteriorating models. Applications of these models to random vibration analysis modeling via simulation and equivalent linearization techniques under Gaussian noise excitation is presented.

Mohammed N. Noori

Papers

Modeling General Hysteresis Behavior and Random Vibration Application