Smart Structures and Systems

  • 제2권4호
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  • Pages.313-320
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  • 2006
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  • 1738-1584(pISSN)
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  • 1738-1991(eISSN)
테크노프레스 (Techno-Press)
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DOI QR코드

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A reliability-based criterion of structural performance for structures with linear damping

  • 투고 : 2006.01.01
  • 심사 : 2006.07.11
  • 발행 : 2006.10.25
⟨ 이전 논문 다음 논문 ⟩

초록

The reliability analysis of structures subjected to stochastic loading involves evaluation of time and probability of the system's residence in a reference domain. In this paper, we derive an asymptotic estimate of exit time for multi-degrees-of-freedom structural systems. The system's dynamics is governed by the Lagrangian equations with linear dissipation and fast additive noise. The logarithmic asymptotic of exit time is found explicitly as a sum of two terms dependent on kinetic and potential energy of the system, respectively. As an example, we estimate exit time and an associated structural performance for a rocking structure.

키워드

참고문헌

  1. Bolotin, V. V. (1984), Random Vibrations of Elastic Systems, Martinus Nijhoff Publishers, The Hague
  2. Fiacco, A. V. and McCormick, G. P. (1990), Nonlinear Programming: Sequential Unconstrained Minimization Techniques, SIAM Classics in Applied Mathematics 4, SIAM, Philadelphia, PA
  3. Freidlin, M. I. and Wentzell, A. D. (1998), Random Perturbations of Dynamical Systems, 2nd Ed., Springer-Verlag, New York
  4. Kovaleva A. (2005), Control of random rocking dynamics of block-like structures. Proceedings of the 3rd European Conference on Structural Control, July 2004. TU Wien, Vienna, Austria
  5. Kovaleva A. (2006a), 'Large deviations estimates of escape time for Lagrangian systems', Proceedings of 44th IEEE Conference on Decision and Control, Seville, Spain
  6. Kovaleva A. (2006b), 'Solution of the exit time problem for mechanical systems with fast noise', Probabilistic Engineering Mechanics (in press)
  7. Kushner, H. J. (1984a), Approximation and Weak Convergence Methods for Random Processes, with Applications to Stochastic System Theory, The MIT Press, Cambridge, MA
  8. Kushner, H. J. (1984b), 'Robustness and approximation of escape time and large deviations estimates for systems with small noise effect', SIAM J. Appl. Math., 44, 160-182 https://doi.org/10.1137/0144012

피인용 문헌

  1. The Melnikov criterion of instability for random rocking dynamics of a rigid block with an attached secondary structure vol.11, pp.1, 2010, https://doi.org/10.1016/j.nonrwa.2008.12.001
  2. Explicit asymptotic solutions for a class of weak-noise escape problems vol.24, pp.1, 2009, https://doi.org/10.1016/j.probengmech.2008.01.002
  3. Control of a weakly perturbed Lagrangian system with a guaranteed escape rate vol.26, pp.1, 2011, https://doi.org/10.1016/j.probengmech.2010.06.005