Equivalent linearization of the Bouc-Wen hysteretic model

Abstract The smooth endochronic hysteretic Bouc–Wen model is studied from the point of view of random vibration. The sources of the errors of the method of equivalent linearization applied to this model using the hypothesis of joint Gaussian behaviour are examined. The method of linearization for softening hysteretic models proposed by the authors, which is based on a combination of Dirac and Gauss densities, is developed and applied to the Bouc–Wen model under a variety of conditions. It is shown that the method gives excellent estimations of the response statistics without increasing the computational effort required by the conventional technique.

[1]  Wilfred D. Iwan,et al.  A generalization of the concept of equivalent linearization , 1973 .

[2]  Robert H. Sues,et al.  Stochastic Evaluation of Seismic Structural Performance , 1985 .

[3]  Chin-Hsun Yeh,et al.  Modeling of nonstationary earthquake ground motion and biaxial and torsional response of inelastic structures , 1989 .

[4]  Wilfred D. Iwan,et al.  The stochastic response of strongly yielding systems , 1988 .

[5]  P. Spanos,et al.  Random vibration and statistical linearization , 1990 .

[6]  Alex H. Barbat,et al.  Improved stochastic linearization method using mixed distributions , 1996 .

[7]  Hiroshi Katukura,et al.  Markovian Hysteretic Characteristics of Structures , 1990 .

[8]  Y. K. Wen,et al.  Stochastic Analysis of Liquefaction Under Earthquake Loading , 1983 .

[9]  Jann N. Yang,et al.  Distribution of Maximum and Statistical Response System , 1981 .

[10]  L. Faravelli,et al.  Stochastic equivalent linearization algorithms and their applicability to hysteretic systems , 1988 .

[11]  Lucia Faravelli,et al.  Stochastic Equivalent Linearization for 3‐D Frames , 1988 .

[12]  R. Clough,et al.  Dynamics Of Structures , 1975 .

[13]  Masanobu Shinozuka,et al.  Simulation of Nonstationary Random Process , 1967 .

[14]  Wilfred D. Iwan,et al.  On the existence and uniqueness of solutions generated by equivalent linearization , 1978 .

[15]  Álvaro Cunha,et al.  The role of the stochastic equivalent linearization method in the analysis of the non‐linear seismic response of building structures , 1994 .

[16]  Zexiang Li,et al.  Stochastic hybrid control of hysteretic structures , 1994 .

[17]  Y. K. Wen,et al.  Method for nonstationary random vibration of inelastic structures , 1994 .

[18]  Goodarz Ahmadi,et al.  Response of base‐isolated buildings to random excitations described by the Clough‐Penzien spectral model , 1989 .

[19]  S. Utku,et al.  Stochastic linearization of multi‐degree‐of‐freedom non‐linear systems , 1976 .

[20]  S. T. Mau,et al.  Systems Identification of Degrading Hysteretic Restoring Forces , 1988 .

[21]  Y. Wen.  Approximate Method for Nonlinear Random Vibration , 1975 .

[22]  Nicolai Minorsky,et al.  Introduction to non-linear mechanics : topological methods, analytical methods, nonlinear resonance, relaxation oscillations , 1947 .

[23]  Thomas T. Baber,et al.  Random Vibration Hysteretic, Degrading Systems , 1981 .

[24]  Yoshiyuki Suzuki,et al.  Stochastic Seismic Response of Hysteretic Structures , 1976 .

[25]  T. Caughey.  Equivalent Linearization Techniques , 1962 .

[26]  Y. J. Park,et al.  EQUIVALENT LINEARIZATION FOR SEISMIC RESPONSES. I: FORMULATION AND ERROR ANALYSIS , 1992 .

[27]  R. Bouc.  Forced Vibration of Mechanical Systems with Hysteresis , 1967 .

[28]  Mohammad Noori,et al.  Equivalent linearization of generally pinching hysteretic, degrading systems , 1996 .

[29]  M. Sakata,et al.  Non-Gaussian equivalent linearization for non-stationary random vibration of hysteretic system , 1994 .

[30]  Lucia Faravelli,et al.  Methods of non-linear stochastic dynamics for the assessment of structural fragility , 1985 .