Stochastic Averaging of Energy Envelope of Bilinear Hysteretic Systems

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Nonlinear Stochastic Dynamic Engineering Systems

Part of the book series: IUTAM Symposium ((IUTAM))

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Abstract

The method of stochastic averaging of energy envelope is applied to predict the response of bilinear hysteretic systems to white noise excitation. The statistics of stationary response for displacement, velocity and energy envelope as functions of excitation level, secondary slope and viscous dam** are analyzed in detail. Comparisons with digital simulation show that the method is superior to other approximate methods have been applied to random response of hysteretic systems.

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References

  1. Caughey, T.K. Random excitation of a system with bilinear hysteresis, J.Appl. Mech., 27 (1960), 649–652.

    MathSciNet  Google Scholar 

  2. Iwan, W.D., and Lutes, L.D., Response of the bilinear hysteretic system to stationary random excitation, J. Acoust. Soc. Am., 43 (1968), 545–552.

    Article  ADS  Google Scholar 

  3. Asano, K., and Iwan, W.D., An alternative approximate to the random response of bilinear hysteretic systems, Earthquake Eng. Struct. Dyn., 12 (1984), 229–236.

    Article  Google Scholar 

  4. Jennings, P.C., Earthquake response of a yielding structure, J. Eng. Mech. Div., ASCE, 91(1965), EM4,41–68.

    Google Scholar 

  5. Iwan, W. D., A Distributed element model for hysteresis and its steady-state dynamic response, J. Appl. Mech., 33 (1966), 893–900.

    Article  ADS  Google Scholar 

  6. WEN, Y.K., Method for random vibration of hysteretic systems, J.Eng. Mech. Div., ASCE, 102(1976), EM2,249–263.

    Google Scholar 

  7. WEN, Y.K., Equivalent linearization for hysteretic system under random excitation, J. Appl. Mech., 47 (1980), 150–154.

    Article  MATH  ADS  Google Scholar 

  8. Iyenger, R.N., and Dash, P.K., Study of the randon vibration of nonlinear systems by the Gaussian closure technique, J. Appl. Mech., 45 (1978), 393–399.

    Article  ADS  Google Scholar 

  9. Roberts, J.B., The response of an oscillator with bilinear hysteresis to stationary random excitation, J.Appl. Mech., 45 (1978), 923–928.

    Google Scholar 

  10. Roberts, J.B., The yielding behaviour of a randomly excited elasto-plastic structure, J. Sound Vib., 72 (1980), 71–85.

    Article  MATH  ADS  Google Scholar 

  11. Stratonovitch, R.L., Topics in the theory of random noise, Vol.1, Gorden and Breach, 1963.

    Google Scholar 

  12. Roberts, J.B., The energy envelope of a randomly excited nonlinear oscillator, J. Sound Vib., 60 (1978), 177–185.

    Article  MATH  ADS  Google Scholar 

  13. Zhu, W.Q., Stochastic averaging of the energy envelope of nearly Lyapunov systems, proc. IUTAM symp. Random vibrations and Reliability, Frankfurt/Oder (GDR) 1982, publish by Akademic-verlag, Berlin (ed. by K.Hennig), 1983, 347–357.

    Google Scholar 

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© 1988 Springer-Verlag Berlin Heidelberg

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Zhu, WQ., Lei, Y. (1988). Stochastic Averaging of Energy Envelope of Bilinear Hysteretic Systems. In: Ziegler, F., Schuëller, G.I. (eds) Nonlinear Stochastic Dynamic Engineering Systems. IUTAM Symposium. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-83334-2_27

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  • DOI: https://doi.org/10.1007/978-3-642-83334-2_27

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-83336-6

  • Online ISBN: 978-3-642-83334-2

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