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Stochastic equivalent linearization algorithms and their applicability to hysteretic systems

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Sommario

Questa memoria riassume alcuni risultati di un progetto di ricerca congiunto: obiettivo di tale progetto è la messa a punto di un metodo di analisi per strutture soggette a carichi dinamici che tenga conto dell'energia dissipata in campo anelastico. La ricerca è concentrata sull'impiego di tecniche di linearizzazione stocastica equivalente. Si dimostra in particolare un teorema che sancisce come condizione necessaria per l'applicabilità del procedimento una descrizione Gaussiana della risposta del sistema. Si analizza, infine, dal punto di vista teorico, la possibilità di impiego di tecniche di analisi module complessa che consentirebbero una definizione dell'eccitazione in termini del suo spettro di risposta.

Summary

This paper summarizes some results of a joint research project aiming at introducing a design procedure of dynamically loaded structures which allows for the energy dissipated in the inelastic range. The joint research is focused on stochastic equivalent linearization techniques. The need of some improvements in the solution scheme arises from the proof of a necessity theorem that limits within a Gaussian description of the response the applicability of the procedure presently adopted. The use of complex modal analysis and, hence, the possibility of making use of a response spectrum description of the loading is also investigated from a theoretical point of view.

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References

  1. Atalik T.S., Utku S.,Stoch. lineariz. of multi-degree-of-freedom nonlinear syst. Earth. Eng. & Struct. Dyn. 4, 411, (1976).

    Google Scholar 

  2. Lin Y.K.,Probabilistic theory of structural dynamics. R.E. Krieger Publ. Comp., N.Y., Ch. 8 (1976).

    Google Scholar 

  3. Caughey T.K.,Nonlinear theory of random vibration. In Adv. in Appl. Mech., Vol. 11, 209, Academic Press (1971).

  4. Wen Y.K.,Approximate method for non-linear random vibration. J. Eng. Mech. Div., Asce EM 101, 389 (1975)'.

    Google Scholar 

  5. Roberts J.B.,The energy envelope of a randomly excited non-linear oscillator. J. Sound and Vibr., 60, 2, 177 (1978).

    Google Scholar 

  6. Roberts J.B.,Energy methods for non-linear systems with non-white excitation. In Henning K. (ed.), Random Vibr. and Reliab., Akademie Verlag, Berlin, 258 (1983).

    Google Scholar 

  7. Zhu W.Q.,On the method of stoch. averaging of energy envelope. In Schueller G.I. (ed.), Proc. Int. Work. Stoch. Struct. Mech., Innsbruck, 17(1982).

  8. Suzuki Y.,Minai R.,Seismic stoch. resp. of state-dep. hyst. struct. Proc. 6th Japan Earth. Eng. Symp., 1169 (1982).

  9. Spencer B.F.,Bergman L.A.,The first passage problem in random vibr. for a simple hysteretic oscillator. Tech. Rep. AAE-85, Univ. of Illinois, (1985).

  10. Iwan W.D., Mason A.B.,Equiv. lin. for systems subjected to non-stat. random excitation. J. Non-Linear Mech., 15, 71 (1980).

    Google Scholar 

  11. Spanos P.,Stoch. lineariz. In Struct. Dyn., Appl. Mech. Rev., 34, 1, 1 (1981).

    Google Scholar 

  12. Crandall S.H.,Perturbation techniques for random vibr. of non-linear systems. J. Acoust. Soc. Amer., 35, 11, 1700 (1963).

    Google Scholar 

  13. Crandall S.H.,Heuristic and equiv. lin. tech. for a random vibration of non-linear oscillators. Proc. 8th Int. Conf. Non-Linear Oscil., Prague, Vol. 1, 211 (1978).

  14. Wu W.F., Lin Y.K.,Cumulant neglect closure for nonlinear oscill. under random parametric and external excit. Int. J. Non-Linear Mech. 4, 349 (1984).

    Google Scholar 

  15. Casciati F., Faravelli L.,Meth. of non-linear stoch. dyn. for the assessment of struct, fragility. Nucl. Eng. Des., 90, 341, (1985).

    Google Scholar 

  16. Casciati F.,Faravelli L.,Reliab. assess, for nonlinear random frames, in Eggwert S. and Lind N.C. (eds.), Prob. Meth. in the Mech. of Solids and Struct., Springer Verlag, 469, (1985).

  17. Casciati F., Faravelli L.,Equiv. Lineariz. in non-linear random vibr. probl. Proc. ICEPV, Xi'an, China (1986).

    Google Scholar 

  18. Lin Y.K., Kozin F., Wen Y.K., Casciati F., Schueller G.I., Der Kiureghian A., Ditlevsen O., Vanmarcke E.,Met. of stoch. struct, dyn. Struct. Safety, 3, 167, (1986).

    Google Scholar 

  19. Wen Y.K.,Equivalent linearization for hysteretic systems under random excitation. J. Appl. Mech., 47, 150, (1980).

    Google Scholar 

  20. Casciati F.,Non linear stochastic dynamics of large structural systems by equivalent linearization. Prof. ICASP 5 (N.C. Lind (ed.)), Vancouver, 1987, 1165, (1987).

  21. Baber T.T., Wen Y.K.,Stochastic response of multist. yielding frames. Earth Eng. and Struct. Dyn. 10, 403, (1982).

    Google Scholar 

  22. Casciati F., Faravelli L.,Non-linear stochastic dynamics by equivalent linearization. In Casciati F. and Faravelli L. (eds.), Methods of Stoch. Struct. Mech., SEAG Pavia, (1986).

    Google Scholar 

  23. Maldonando G.O.,Singh M.P.,Casciati F.,Faravelli L.,Stochastic response of single degree of freedom hysteretic oscillators. Rep. VPI-E-87-5, Blacksburg, VA, (1987).

  24. Casciati F., Faravelli L.,Stochastic equiv. lin. in 3-D hysteretic frames. Proc. 9th SMiRT, Vol. M, 453, (1987).

    Google Scholar 

  25. Casciati F., Faravelli L.,Stochastic linearization for 3D frames. J. of Eng. Mechanics, ASCE, 10, (1988).

    Google Scholar 

  26. Chen X-W.,About Atalik and Utku's linearization technique, Innsbruck, (1987).

  27. Kozin F.,Personal communication, (1987).

  28. Casciati F.,Equivalent linearization technique in the analysis of seismic excited structures. Proc. Euro-China Joint Seminar on Earth. Eng., Beijing, (1986).

  29. Kozin F.,Personal communication, (1985).

  30. Kozin F.,Comments upon the techniques of statistical lin., Proc. of Annual Meeting of Jap. Assoc. of Autom. Control. Eng., Osaka, (1965).

  31. Kozin F.,Parameter estimation and statistical linearization, US-Austria Joint Seminar, Boca Raton, (1987).

  32. Bruckner A.,Lin Y.K.,Generalization of the equivalent linearization method for non-linear random vibration problems. Rep. CAS86-2, Florida Atlantic Univ., (1986).

  33. Bartels R.H.,Stewart G.W.,Sol. of the matrix eq. AX++XB=Calgorithm 432, Comm. ACM, 15, 9, 820, (1972).

  34. Meirovitch L.,Elem. of vibr. analysis. McGraw Hill, (1986).

  35. Singh M.P., Mehta K.B.,Seismic design resp. by an alt. SRSS rule. Earth. Eng. and Struct. Dyn. 11, 771, (1983).

    Google Scholar 

  36. Mochio T.,Samaras E.,Shinozuka M.,Stochastic equivalent linearization for finite-element based reliability analysis. Proc. ICOSSAR '85, Kobe, I 375, (1985).

  37. Baber T.T.,Modal analysis for random vibration of hysteretic frames. Earthquake Eng. and Struct. Dyn., 14, 841, (1986).

    Google Scholar 

  38. Der Kiureghian A.,A seismic response spectrum method for random vibration analysis of MDOF systems. Earth Eng. and Struct. Dyn. 9, 419, (1981).

    Google Scholar 

  39. Singh M.P.,Maldonado G.,Heller R.,Faravelli L.,Modal analysis of non-linear hysteretic structures for seismic motions IUTAM Symp. on Non-Linear Stoch. Dyn. Eng. Syst., Ingls, (1987); Springer-Verlag, 443, (1988).

  40. Roberts J.B., Spanos P.,Stochastic Averaging: An Approximate Method of Solving Random Vibration Problems, Int. J. of Non-Linear Mechanics, Vol. 21, 2, 111, (1986).

    Google Scholar 

  41. Spanos P.,Formulation of Stochastic Linearization for Symmetric or Asymmetric MDOF System, J. of Applied Mechanics, ASME, 47, 209, (1980).

    Google Scholar 

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Faravelli, L., Casciati, F. & Singh, M.P. Stochastic equivalent linearization algorithms and their applicability to hysteretic systems. Meccanica 23, 107–112 (1988). https://doi.org/10.1007/BF01556709

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  • DOI: https://doi.org/10.1007/BF01556709

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