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Exact stationary response solutions of nonlinear dynamic systems

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Summary

Exact stationary solutions are constructed for nonlinear dynamic systems subjected to stochastic excitation. The results are then applied to both classical and nonclassical stochastic vibration systems.

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References

  1. Crandall, S. H.;Zhu, W. Q.: Random vibration: A survey of recent developments. Trans. ASME/J. Appl. Mech. 50 (1983) 953–962

    Google Scholar 

  2. Cai, G. Q.;Lin, Y. K.: On exact stationary solutions of equivalent nonlinear stochastic systems. Int. J. nonlinear Mech. 23 (1988) 315–325

    Google Scholar 

  3. Cai, G. Q.;Lin, Y. K.: A new approximate solution technique for randomly excited nonlinear oscillators — II. Int. J. nonlinear. Mech. 27 (1992) 969–979

    Google Scholar 

  4. Caughey, T. K.: Nonlinear theory of random vibrations. Advances Appl. Mech. 11. New York: Academic Press 1971

    Google Scholar 

  5. Bharucha-Reid, A. T.: Elements of the theory of Morkov Process and their applications. New York: McGraw-Hill 1960

    Google Scholar 

  6. Caughey, T. K.;Ma, F.: The exact steady-state solution of a class of nonlinear stochastic systems. Int. J. nonlinear Mech. 17 (1982) 137–147

    Google Scholar 

  7. Caughey, T. K.;Ma, F.: The steady-state response of a class of dynamic systems to stochastic excitation. Trans. ASME/J. Appl. Mech. 49 (1982) 629–632

    Google Scholar 

  8. Nigam, N. C.: Introduction to random vibrations. Cambridge, Massachusetts: The MIT Press 1983

    Google Scholar 

  9. Zhang, Zh.; Wang, R.; Kusumoto, S.: A mathematical demonstration of nonlinear systems of existing exact stationary solutions under stochastic excitations. (submitted to Probability Engineering Mechanics)

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Wang, R., Kusumoto, S. & Zhang, Z. Exact stationary response solutions of nonlinear dynamic systems. Arch. Appl. Mech. 66, 255–263 (1996). https://doi.org/10.1007/BF00787353

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  • DOI: https://doi.org/10.1007/BF00787353

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