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Application of the polynomial chaos approximation to a stochastic parametric vibrations problem

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Języki publikacji
EN
Abstrakty
EN
In the paper the application of the polynomial chaos expansion in case of parametric vibrations problem is presented. Hitherto this innovative approach has not been applied to such a stochastic problem. The phenomenon is described by a nonlinear ordinary differential equation with periodic coefficients. It can be observed among others in cable-stayed bridges due to periodic excitation caused by a deck or a pylon. The analysis is focused on a real situation for which the problem of parametric resonance was observed (a cable of the Ben–Ahin bridge). The characteristic of the viscous damper is considered as a log-normal random variable. The results obtained by the use of the polynomial chaos approximations are compared with the ones based on the Monte Carlo simulation. The convergence of both methods is discussed. It is found that the polynomial chaos yields a better convergence then the Monte Carlo simulation, if resonant vibrations appear.
Rocznik
Strony
220--228
Opis fizyczny
Bibliogr. 27 poz., tab., wykr.
Twórcy
  • Faculty of Civil Engineering, Wrocław University of Technology, Wybrzeże Wyspiańskiego 27, 50-370 Wrocław, Poland, aneta.brzakala@pwr.wroc.pl
Bibliografia
  • [1] R.G. Ghamen, P.D. Spanos, Stochastic Finite Elements: A Spectral Approach, Springer-Verlag, New York, 1991.
  • [2] M. Anders, M. Hori, Stochastic finite element method for elasto-plastic body, International Journal for Numerical Methods in Engineering 46 (1999) 1897–1916.
  • [3] R.G. Ghanem, P.D. Spanos, Stochastic Galerkin expansion for nonlinear random vibration analysis, Probabilistic Engineering Mechanics 8 (1993) 255–264.
  • [4] A. Sarkar, R.G. Ghanem, Mid-frequency structural dynamics with parameter uncertainty, Computer Methods in Applied Mechanics and Engineering 191 (2002) 5499–5531.
  • [5] O. Le Maitre, O. Knio, H. Najm, R. Ghanem, A stochastic projection method for fluid flow: basic formulation, Journal of Computational Physics 173 (2001) 481–511.
  • [6] G. Manolis, C. Karakostas, A. Green’s, function method to SH-wave motion in random continuum, Engineering Analysis with Boundary Elements 27 (2003) 93–100.
  • [7] D. Xiu, G. Karniadakis, Stochastic modelling of flow-structure interactions using generalized polynomial chaos, Journal of Fluids Engineering 124 (2002) 51–59.
  • [8] D. Xiu, G. Karniadakis, The Wiener-Askey polynomial chaos for stochastic differential equations, SIAM Journal on Scientific Computing 24 (2002) 619–644.
  • [9] D. Xiu, G. Karniadakis, A new stochastic approach to transient heat conduction modelling with uncertainty, International Journal of Heat and Mass Transfer 46 (2003) 4681–4693.
  • [10] O. Le Maitre, O. Knio, H. Najm, R. Ghanem, Uncertainty propagation using Wiener–Haar expansions, Journal of Computational Physics 197 (2004) 28–57.
  • [11] O. Le Maitre, H. Najm, R. Ghanem, O. Knio, Multiresolution analysis of Wiener-type uncertainty propagation schemes, Journal of Computational Physics 197 (2004) 502–531.
  • [12] D. Xiu, G. Karniadakis, Modelling uncertainty in steady-state diffusion problems via generalized polynomial chaos, Computer Methods in Applied Mechanics and Engineering 191 (2002) 4927–4948.
  • [13] D. Xiu, G. Karniadakis, Modelling uncertainty in flow simulations via generalized polynomial chaos, Journal of Computational Physics 187 (2003) 137–167.
  • [14] J. Langer, Dynamika budowli, Wydawnictwo Politechniki Wrocławskiej, Wrocław, 1980. (in Polish).
  • [15] E. Caetano, Cable Vibrations in Cable-Stayed Bridges, Structural Engineering Documents 9, International Association for Bridge and Structural Engineering IABSE, 2007.
  • [16] J.L. Lilien, A. Pinto Da Costa, Vibration amplitudes caused by parametric excitation of cable stayed structures, Journal of Sound and Vibration 174 (1) (1994) 69–90.
  • [17] G.F. Royer-Carafangi, Parametric-resonance-induced vibrations in network cable-stayed bridges. A continuum approach, Journal of Sound and Vibration 262 (2003) 1191–1222.
  • [18] Q. Zhou, S.R.K. Nielsen, W.L. Qu, Semi-active control of three-dimensional vibration of an inclined sag cable with magnetho-rheological dampers, Journal of Sound and Vibration 296 (2006) 1–22.
  • [19] K. Takahashi, Dynamic stability of cables subjected to an axial periodic load, Journal of Sound and Vibration 144 (2) (1991) 323–330.
  • [20] A. Brząkała, Analiza drgań parametrycznych want mostowych w ujęciu deterministycznym i stochastycznym, Raport serii PRE nr 1/2011, Ph.D. Thesis. (in Polish).
  • [21] C.T. Georgakis, C.A. Taylor, Nonlinear dynamics of cable stays. Part I: sinusoidal cable support excitation, Journal of Sound and Vibration 281 (2005) 537–564.
  • [22] J. Hajduk, J. Osiecki, Ustroje cięgnowe. Teoria i obliczanie, Wydawnictwa Naukowo-Techniczne, Warszawa, 1970 (in Polish).
  • [23] M. Irvine, Cable Structures, Dover Publications, Inc., New York, 1981.
  • [24] Q. Zhou, S.R.K. Nielsen, W.L. Qu, Semi-active control of three-dimensional vibration of an inclined sag cable with magnetho-rheological dampers, Journal of Sound and Vibration 296 (2006) 1–22.
  • [25] Q. Zhou, S.R.K. Nielsen, W.L. Qu, Semi-active control of shallow cables with magnethoreological dampers under harmonic axial support motion, Journal of Sound and Vibration 311 (2008) 683–706.
  • [26] Z. Yu, Y.L. Xu, Mitigation of three-dimensional vibration of inclined sag cable using discrete oil dampers I. Formulation, Journal of Sound and Vibration 214 (4) (1998) 659–673.
  • [27] Z. Yu, Y.L. Xu, Mitigation of three-dimensional vibration of inclined sag cable using discrete oil dampers II. Application, Journal of Sound and Vibration 214 (4) (1998) 675–693.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-d68b4dc0-f907-40da-b124-c8d6c42acc96
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