Stochastic dynamics and reliability of degrading systems

• Autorzy: Sobczyk K.
• Języki publikacji: EN

Abstrakty

EN

In this paper the basic methodology of the coupled response-degradation modelling of stochastic dynamical systems is presented along with the effective analysis of selected problems. First, the general formulation of the problems of stochastic dynamic s coupled with the evolution of deterioration process is given. Then same specific degrading oscillatory systems under random excitation are analyzed with a special attention on the systems with fatigue-induced stiffness degradation. Both, the general discussion and the analysis of seleeted exemplary problems indicate how the reliability of deteriorating stochastic dynamical systems can be assessed.

Słowa kluczowe

EN

stochastic dynamics; fatigue induced stiffness degradation; hysteretic systems; systems with varying/random structure

• Wydawca: Polska Akademia Nauk, Wydział IV Nauk Technicznych
• Czasopismo: Bulletin of the Polish Academy of Sciences. Technical Sciences
• Rocznik: 2006
• Tom: Vol. 54, nr 1
• Strony: 125--137
• Opis fizyczny: Bibliogr. 37 poz., 7 rys.

Twórcy

autor

Sobczyk K.

• Department of Dynamics of Complex Systems, Institute of Fundamental Technological Research, Polish Academy of Sciences, 21 Świętokrzyska St., 00-049 Warsaw, Poland,

Bibliografia

• [1] K. Sobczyk, Stochastic Differential Equations with Applications to Physics and Engineering, Kluwer Acad. Publ., Dordrecht, 1991.
• [2] T.T. Soong and M. Grigoriu, Random Vibrations of Structural and Mechanical Systems, Prentice Hall, New Jersey, 1993.
• [3] Y.K. Lin and G.Q. Cai, Advanced Probabilistic Dynamics, McGraw Hill, New York, 1995.
• [4] K. Sobczyk and B.F. Spencer, Random Fatigue: From Data to Theory, Academic Press, Boston, 1992.
• [5] J.B. Roberts, "The response of an oscillator with bilinear hysteresis to stationary random excitation", ASME J. Appl. Mechanics 45, 923-928 (1978).
• [6] Y.K. Wen, "Stochastic response and damage analysis of inelastic structures", Probabilistic Eng. Mech. 1,57-69 (1986).
• [7] M. Grigoriu, "Reliability of degrading systems", Structural Safety 8, 345-351 (1990).
• [8] K. Sobczyk and J. Trębicki, "Stochastic response of degrading stochastic systems", in Rheology of Bodies with Defects (ed. R. Wang), Proc. IUTAM Symp., Kluwer Acad. Publ., Dordrecht, 1999.
• [9] K. Sobczyk and J. Trębicki, "Stochastic dynamics with fatigue induced stiffness degradation", Probabilistic Eng. Mech. 15, 91-99 (2000).
• [10] R.L. Grossmayer, "Elastic-plastic oscillators under random excitation", J. Sound and Vibration 65 (3), 353-379 (1979).
• [11] K. Sobczyk and J. Trębicki, "Modelling of random fatigue by cumulative jump processes", Eng. Fract. Mechanics 34 (2), 477-493 (1989).
• [12] M. Grigoriu, "Reliability of Daniels systems subject to quasistatic and dynamic nonstationary Gaussian load processes", Probabilistic Eng. Mech. 4 (3),128-134 (1989).
• [13] Rychlik and M. Grigoriu, "Reliability of Daniels systems with equal load sharing rule subject to stationary Gaussian dynamic loads", Probabilistic Eng. Mech. 7, 113-121 (1992).
• [14] K. Sobczyk, "On cumulative jump model s for random deterioration processes", Annals Universitatis M. Curie-Sklodowska Lublin, Vol. LI, 15, Sec. A, 145-157 (1997).
• [15] Y. Suzuki and R. Minai, "Application of stochastic differential equations to seismic reliability analysis of hysteretic structures", Probabilistic Eng. Mech. 3 (1), (1988).
• [16] J.B. Roberts, "The yielding behaviour of a randomly excited elasto-plastic structure", J. Sound and Vibration 72 (1), 71-85 (1980).
• [17] P.D. Spanos, "Hysteretic structural vibrations under random load", J. Acoust. Soc. Amer. 65,404-410 (1979).
• [18] P. Cawley and R.D. Adams, 'The location of defects in structures from measurements of natural frequencies", J. Strain Analysis 14,49-57 (1979).
• [19] T.G. Chondras, A.D. Dimaroganas, and J. Yao, "A continuous cracked beam vibration theory", J. Sound and Vibration 215 (1), 17-34 (1998).
• [20] J. Grasman and H. Roozen, "Reliability of stochastically forced systems", in Road- Vehicle-Systems and Related Mathematics (Ed. H. Neunzert, pp. 219-235), Kluwer Acad. Publ., 1989.
• [21] C.W. Gardiner, Handbook of Stochastic Methods for Physics, Chemistry and the Natural Sciences, Springer, Berlin, 1985.
• [22] Y. Kondo, "Prediction of fatigue crack initiation life based on a pit growth", Corrosion 45 (1), 7-11 (1989).
• [23] S. Kocańda, Fatigue Fracture, WNT, Warszawa, 1985, (in Polish).
• [24] K. Sobczyk, "Modelling of random fatigue crack growth", Eng. Fracture Mechanics 24 (4), 609-623 (1986).
• [25] H.O. Madsen, S. Krenk, and N.C. Lind, Methods of Structural Safety, Prentice Hall, New Jersey, 1986.
• [26] K. Sobczyk and J. Trębicki, "Maximum entropy principle and nonlinear stochastic oscillators", Physica A 193,448-468 (1993).
• [27] J. Trębicki and K. Sobczyk, "Maximum entropy principle and non-stationary distributions of stochastic systems", Probabilistic Eng. Mech. 11,169-178 (1996).
• [28] J. Lemaitre and J.L. Chaboche, Mechanics of Solid Materials, Cambridge Univ. Press, Cambridge, 1990.
• [29] K. Sobczyk and J. Trębicki, "On stochastic dynamic systems with degradation", Studies in Structural Mechanics, Cracow University of Technology, 302, 245-254 (2004), (in Polish).
• [30] G.E. Dieter, Mechanical Behaviour of Metals under Tension, McGraw Hill, New York, 1976.
• [31] S.W. Jemielianov, Theory of Systems with Varying Structure, Nauka, Moscow, 1970, (in Russian).
• [32] J. Trębicki, Stochastic Analysis of Vibratory Systems with Variable Structure, PhD Thesis, Inst. Fund. Technol. Res., Polish Academy of Sciences, Warsaw, 1996, (in Polish).
• [33] C. Jogrens, Methods for Analysis of Switching Stochastic Systems, PhD Thesis, Dept. of Math. Statistics, Lund University, Sweden, 1991.
• [34] W. Yang and Z. Suo, "Global view of microstructural evolution: energetics, kinetics and dynamical systems", Acta Mech. Sinica 12, 144-157 (1996).
• [35] Z. Suo, "Evolving material structures of small feature sizes", Int. J. Solids and Structures 37, 367-378 (2000).
• [36] K. Sobczyk, J. Trębicki, and A.B. Movchan, "Crack path in an elastic material with a random array of small defects", Int. J. Fracture 125, 103-123 (2004).
• [37] M. Ciarletta, G. Iovane, and M.A. Sumbatyan, "On stress analysis for cracks in elastic materials with voids", Int. J. Eng. Science 41, 2447-2461 (2003).