Summary
A thorough non-Gaussian stationary analysis of a nondimensionalized form of a Bouc-Wen-Baber smooth hysteresis model is presented. Stationary moments of up to 6th order are generated via 3000 sample Monte Carlo simulation in order to assess the convergence of the non-Gaussian response statistics. The degree of deviation from Gaussian response is assessed by comparison of the simulated probability density functions of various response variables with a corresponding unit normal density function. The effect of variation of hysteresis shape control parameters and other important system and excitation parameters, such as the postyield to preyield stiffness ratio, and power spectral density level on response coordinate moments of various orders is studied. The effect of these parameters on correlation coefficients, probability density of the displacement, and other statistical indices are thoroughly studied. This study provides considerable insight about the range of important system and excitation parameters influencing system response. These information on the characteristic behaviors of BWB hysteresis model is useful for non-Gaussian analysis of MDOF hysteresis models and comparative studies with approximation techniques.
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References
Baber, T.T. and Wen, Y.K.: Stochastic Response of Multistory Yielding Frames. J. of Earthq. Eng. and Struc. Dyn., 1982, (10), 403–416.
Baber, T.T.: Nonzero Mean Random Vibration of Hysteretic Systems. ASCE, J. of Eng. Mech. 1984, (110), 1036–1049.
Baber, T.T.: Nonzero Mean Random Vibration of Hysteretic Frames. Computers and Structures, 1986, (23), 265–277.
Baber, T.T. and Noori, M.: Random Vibration of Degrading, Pinching Systems. ASCE, J. of Eng. Mech., 1985, (111), 1010–1027.
Baber, T.T. and Noori, M.: Modeling General Hysteresis Behavior and Random Vibration Application. Trans. of ASME, J. of Vib., Acous., Str., and Rel.in Des., 1986, (108), 411–420.
Casciati, F. and Faravelli, L.: Stochastic equivalent linearization in 3-D hysteretic frames. Trans. of 9th Int. Conf. on Struc. Mech. in Reactor Technology, 1987, (M), pp 453–458.
Casciati, F. and Faravelli, L.: Non-linear seismic analysis of three-dimensional frames. Proc. of Int. Conf. on Des., Const. and Repair of Building Structures in Earthq. Zone, 1987, 104–108.
Davoodi, H. and Noori, M.N.: Extension of An Ito-Based Approximation Technique for Random Vibration of A BBW General Hysteresis Model, Part II: Non-Gaussian Analysis. J. of Sound and Vib., 1990, (139), No. 3.
Minami, T. and Osawa, Y.: Elastic-Plastic Response Spectra for Different Hysteretic Rules. Earthq. Eng. and Struc. Dyn., 1988 (16), 555–568.
Noori, M., Davoodi, H. and Choi, J.D.: Zero and Nonzero Mean Random Vibration Analysis of a New General Hysteresis Model. J. of Prob. Eng. Mech., 1986, (4), 192–201.
Noori, M. and Padula, M.: Application of A New Approximation Method To Random Vibration of A General Hysteresis. Journal of Nonlinear Dynamics (to appear).
Noori, M.N., Davoodi, H. and Saffar, A.: An Ito-Based General Approximation Method for Random Vibration of Hysteretic Systems, Part I: Gaussian Analysis. J. of Sound and Vib., 1988, (127), No. 2, 331–342.
Noori, M.N., Davoodi, H.: Comparison Between Equivalent Linearization and Gaussian Closure for Random Vibration of Several Nonlinear Systems. Int. J. of Eng. Science, 1990, (28), No. 9, 897–905.
Roberts, J.B. and Spanos, P.D.: Random Vibration and Statistical Linearization, 1990, John Wiley and Sons, New York.
Thyagarajan, R.S.: Modeling and Analysis of Hysteretic Structural Behavior. Report No. EERL 89-03, Caltech Pasadena, California, 1989.
Wen, Y. K.: Method for Random Vibration of Hysteretic Systems. J. of the Eng. Mech. Div., ASCE, 1976, (102), EM2, 249–263.
Wen, Y.K.: Methods of Random Vibration for Inelastic Structures. Appl. Mech. Rev., 1989, (42), No. 2, 39–52
Bouc, R.: Modele Mathematique d’Hysteresis. Acustica, 1961, (24), 16–25, Marseille, France.
Mohammadi, J. and Amin, M.: Nonlinear Stochastic Finite Element Analysis of Pipes on Hysteretic Supports Under Seismic Excitation. Comp. Prob. Meth., Proc. of The Joint ASME/SES Conf., 1988, Berkeley, California, AMD 93, 123–133.
Simulescu, I., Mochio, T. and Shinozuka, M.: Equivalent Linearization Method in Nonlinear FEM. ASCE, J. of Eng. Mech., 1989, pp 475–492.
Constantinou, M.C. and Tadjbakhsh, I.G.: Hysteretic Dampers in Base Isolation: Random Approach. ASCE, J. of Struc. Eng., 1985, (4), 705–721.
Igusa, T.: Response Characteristics of an Inelastic Two-Degree-of-Freedom Primary-Secondary System. Report No. 87-7/TI-01, Department of Civil Eng., Northwestern University, 1987.
Su, L., Ahmadi, G. and Tadjabaksh I.G.: A Comparative Study of Different Base Isolators. Proc. of ASCE, Struc. Congress 87, 1987, Orlando, Florida. 15–26.
Mohammad Yar, A. and Hammond, T.: Modelling and Response of Bilinear Hysteretic Systems. ASCE, J. of Eng. Mech., 1987, (113), 1000–1013.
Orabi, I., Ahmadi, G. and Su, L.: Hysteretic Column under Earthquake Excitations. ASCE, J. of Eng. Mech., 1989, (1), 33–51.
Wu, W.F. and Lin, Y.K.: Cumulant-Neglect Closure for Nonlinear Oscillators Under Random Parametric and 8External Excitations. Int. J. of Nonl. Mech., 1984, (19), 349–362.
Minai, R. and Suzuki, Y.: Stochastic Estimate and Control of Hysteretic Structural Systems. Presented at the Second International Conference on Stochastic Structural Dynamics, Boca Raton, FL, May 9–11, 1990.
Yang, C.Y., Cheng, A.H. and Roy, V.: Chaotic and Stochastic Dynamics for a Nonlinear Structure with Hysteresis and Degradation. J. of Prob. Eng. Mech. (To Appear).
Park, Y.J., Wen Y.K and Ang, A.H-S.: Random Vibration of Hysteretic Systems Under Bi-Directional Ground Motions. Earth. Eng. and Struc. Dyn., 1986, (14), 543–557.
Spanos, P-T.: Stochastic Analysis of An Osci llator with Non-Linear Damping, Int. J. of Nonl. Mech., 1978, (13), 249–259.
Spanos, P-T.: Formulation of Stochastic Linearization for Symmetric or Assymetric MDOF Nonlinear Systems. Trans. of ASME, J. of Appl. Mech., 1980, (1), 209–211.
Spanos, P-T.: Stochastic Linearization in Structural Dynamics. Applied Mech. Rev., 1981, (1), 1–8.
Sues, R.H., Wen Y.K. and Ang, A.H-S.: Safety Evaluation of Structures to Earthquakes. ASCE, Proc. of the Symp. on Prob. Meth. in Struc. Eng., 1981, St. Louis, Missouri., 358–377.
Wen, Y.K.: Stochastic Response and Damage Analysis of Inelastic Structures. J. of Prob. Eng. Mech., 1986, (1), No. 1, pp 49–57.
Hampl, N.C., and Schuller, G.I.: Probability Densities of the Response of Nonlinear Structures Under Stochastic Dynamic Excitation. J. of Probabilistic Engineering Mechanics, 1989, (4), No. 1, 2–9.
Lin, Y.K.: A New Solution Technique For Randomly Excited Hysteretic Structures. Technical Report NCEER-88-0012, Center for Applied Stochastic Research, Boca Raton, Florida, 1988.
Liu, Q.: Response Analysis of a Hysteretic System Under Random Excitation. Department of Mechanical Engineering, University of New Brunswick, Canada, 1990.
Ibrahim, R.A.: Parametric Random Vibration, Letchworth, Hertfordshire, England: Research Studies Press Ltd, 1985.
Ibrahim, R.A., Soundararajan, A. and Heo, H.: Stochastic Response of Nonlinear Dynamic Systems Based on Non-Gaussian Closure. Trans. of the ASME, J. of Appl. Mech., 1985, (52), 965–970.
Crandall, S.H.: Non-Gaussian Closure for Random Vibration of a Non-Linear Oscillator. Int. J. of Nonlinear Mechanics, 1980, (20), 303–313.
Fan, F.G., and Ahmadi, G.: Loss of Accuracy and Nonuniqueness of Sound and Vibration of Solutions Generated by Equivalent Linearization and Cumulant-Neglect Methods. (To Appear).
Sun, J.Q., and Hsu, C.S.: Cumulant-Neglect Closure Method for Nonlinear Systems Under Random Excitations. ASME Journal of Applied Mechanics, 1987, (54), 649–655.
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Noori, M., Davoodi, H., Baber, T.T. (1992). A Comprehensive Stationary Non-Gaussian Analysis of BWB Hysteresis. In: Bellomo, N., Casciati, F. (eds) Nonlinear Stochastic Mechanics. IUTAM Symposia. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-84789-9_36
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DOI: https://doi.org/10.1007/978-3-642-84789-9_36
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