Abstract
An approximate method for analyzing the response of nonlinear systems with the Preisach hysteresis of the non-local memory under a stationary Gaussian excitation is presented based on the covariance and switching probability analysis. The covariance matrix equation of the Preisach hysteretic system response is derived. The cross correlation function of the Preisach hysteretic force and response in the covariance equation is evaluated by the switching probability analysis and the Gaussian approximation to the response process. Then an explicit expression of the correlation function is given for the case of symmetric Preisach weighting functions. The numerical result obtained is in good agreement with that from the digital simulation.
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References
Krasnoselskii MA, Pokrovskii AV. Systems with Hysteresis. Berlin: Springer, 1989
Cai GQ, Lin YK. On randomly excited hysteretic structures.ASME J Appl Mech, 1990, 57: 442–448
Hughes D, Wen JT. Preisach modeling of piezoceramic and shape memory alloy hysteresis.Smart Materials Struct, 1997, 6: 287–300
Wen YK. Method for random vibration of hysteretic systems.ASCE J Engrg Mech Div, 1976, 102: 249–263
Dahl PK. Solid friction damping of mechanical vibrations.AIAA J, 1976, 14: 1675–1682
Yar M, Hammond JK. Modeling and response of bilinear hysteretic systems.ASCE J Engrg Mech, 1987, 113: 1000–1013
Song GQ, Sun QP, Hwang KC. Effect of microstructure on the hardening and softening behaviors of polycrystalline shape memory alloys, part I: micromechanics constitutive modeling.Acta Mechanica Sinica, 2000, 16: 309–324
Macki JW, Nistri P, Zecca P. Mathematical models for hysteresis.SIAM Rev, 1993, 35: 94–123
Zhu WQ, Cai GQ. Nonlinear stochastic dynamics: a survey of recent developments.Acta Mechanica Sinica, 2002, 18: 551–566
Caughey TK. Equivalent linearization techniques.J Acous Soc Amer, 1963, 35: 1706–1711
Roberts JB, Spanos PD. Random vibration and statistical linearization. Chichester: Wiley, 1990
Roberts JB, Spanos PD. Stochastic averaging: an approximate method of solving random vibration problems.Int J Non-Linear Mech, 1986, 21: 111–134
Zhu WQ. Stochastic averaging methods in random vibration.ASME Appl Mech Rev, 1988, 41: 189–199
Roberts JB. Application of averaging methods to randomly excited hysteretic systems. In: Ziegler F and Schueller L eds. Nonlinear Stochastic Dyn Engrg Sys. Berlin: Springer-Verlag, 1988. 361–379
Wen YK. Equivalent linearization for hysteretic systems under random excitation.ASME J Appl Mech, 1980, 47: 150–154
Zhu WQ, Lin YK. Stochastic averaging of energy envelope.ASCE J Engrg Mech, 1991, 117: 1890–1905
Mayergoyz ID, Korman CE. The Preisach model with stochastic input as a model for aftereffect.J Appl Phy, 1994, 75: 5478–5480
Korman CE, Mayergoyz ID. Switching as an exit problem.IEEE Trans Mag, 1995, 31: 3545–3547
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The project supported by the National Natural Science Foundation of China (19972059) and Zhejiang Provincial Natural Science Foundation (101046)
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Zuguang, Y. Response analysis of randomly excited nonlinear systems with symmetric weighting Preisach hysteresis. Acta Mech Sinica 19, 365–370 (2003). https://doi.org/10.1007/BF02487814
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DOI: https://doi.org/10.1007/BF02487814