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Treatment of Constrained Multibody Dynamic Systems with Uncertainties
Technical Paper
2005-01-0936
ISSN: 0148-7191, e-ISSN: 2688-3627
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English
Abstract
This study addresses the critical need for computational tools to model complex nonlinear multibody dynamic systems in the presence of parametric and external uncertainty. Polynomial chaos has been used extensively to model uncertainties in structural mechanics and in fluids, but to our knowledge they have yet to be applied to multibody dynamic simulations. We show that the method can be successfully applied to quantify uncertainties in time domain and frequency domain for constrained multibody dynamic systems.
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Authors
Citation
Sandu, C., Sandu, A., Chan, B., and Ahmadian, M., "Treatment of Constrained Multibody Dynamic Systems with Uncertainties," SAE Technical Paper 2005-01-0936, 2005, https://doi.org/10.4271/2005-01-0936.Also In
References
- Bergin M Milford J.B. “Application of Bayesian Monte Carlo Analysis to a Lagrangian Photochemical Air Quality Model” Atmos. Env. 34 5 781 792 Jan. 2000
- Bergin, M.S. Noblet, G.S. Petrini, K. Dhieux, J.R. Milford, J.B. Harley, R.A. “Formal Uncertainty Analysis of a Lagrangian Photochemical Air Pollution Model” Environ. Sci. Technol. 33 1116 1126 1999
- Butler, D.M. “The Uncertainty in Ozone Calculations by a Stratospheric Photochemistry Model” Geophys. Res. Lett. 5 769 772 1978
- Cai, G.Q. Lin, Y.K. Elishakoff, I. “A New Approximate Solution Technique for Randomly Excited Non-linear Oscillators” Int. J. of Non-linear Mechanics 27 6 969 979 1992
- Caughey, T.K. “ Nonlinear Theory of Random Vibrations ” Advances in Applied Mechanics 11 Academic Press New York 1971
- Crandall, S.H. “Non-Gaussian Closure Techniques for Stationary Random Vibration,” Int. J. of Nonlinear-Mechanics 20 1 1 8 1985
- Dimentberg, M.F. “An exact Solution to a Certain Non-linear Random Vibration Problem” Int. J. of Non-linear Mechanics 17 4 231 235 1982
- Dunker, A.M. “The Decoupled Direct Method for Calculating Sensitivity Coefficients in Chemical Kinetics” J. Chemical Physics 81 2385 1984
- Evensen, G. “Sequential data assimilation with a nonlinear quasi-geostrophic model using Monte-Carlo methods to forecast error statistics” J. of Geophys. Res. 99 C5 1994
- Falsone, G. “Stochastic Linearization of MDOF Systems under Parametric Excitations” Int. J. of Non-linear Mechanics 27 6 1025 1037 1992
- Ghanem, R. Sarkar, A. “Reduced Models for the Medium-Frequency Dynamics of Stochastic Systems” J. of Acoust. Soc. Am. 113 1 Feb. 2003
- Ghanem, R. Spanos, P. Stochastic Finite Elements: A Spectral Approach Springer Verlag 1991
- Ghanem, R. Spanos, P. Swerdon, S. “Coupled in-line and transverse flow-induced vibration: higher order harmonic solutions” Sadhana, J. the Indian Academy of Sciences 20 2-4 691 707 Aug 1995
- Ghanem, R. Spanos, P. “A stochastic Galerkin expansion for nonlinear random vibration analysis” Probabilistic Engineering Mechanics 8 255 264 1993
- Ghanem, R. Spanos, P. “A Spectral Stochastic Finite Element Formulation for Reliability Analysis” J. of Engineering Mechanics, ASCE 117 10 2351 2372 Oct. 1991
- Ghanem, R. Spanos, P. “Polynomial Chaos in Stochastic Finite Element” J.of Applied Mechanics, ASME 57 1 197 202 March 1990
- Isukapalli, S.S. Georgopoulos, P.G. “Development and Application of Methods for Assessing Uncertainty in Photochemical Air Quality Problems” Interim Report 1998
- Isukapalli, S.S. Georgopoulos, P.G. “Propagation of Uncertainties in Photochemical Mechanisms through Urban/Regional Scale Grid-Based Air Pollution Models” Proc. of the A&WMA 90th Annual meeting Toronto, Canada June 1997
- Isukapalli, S.S. Georgopoulos, P.G. “Computationally Efficient Methods for Uncertainty Analysis of Environmental Models” Proc. of the A&WMA specialty conference on Computing in Environmental Resource Management 656 665 1997
- Isukapalli, S.S. Roy, A. Georgopoulos, P.G. “Stochastic Response Surface Methods (SRSMs) for Uncertainty Propoagation: Application to Environmental and Biological Systems” Feb. 1998
- Jardak, M. Su, C.-H. Karniadakis, G.E. “Spectral Polynomial Chaos Solutions of the Stochastic Advection Equation” J. Sci. Comp. 17 1-4 319 338 2002
- Karniadakis, G.E. “Towards a numerical error bar in CFD” J. Fluids Eng. March 1995
- Lucor, D. Xiu, D. Su, C.-H. Karniadakis, G.E. “Predictability and Uncertainty in CFD” Int. J. Num. Meth. Fluids 43 4 485 505 Oct. 20 2003
- Lucor, D. Su, C-H. Karniadakis, G.E. “Generalized Polynomial Chaos and Random Oscillators” Int. J. for Num.l Meth. in Engineering 2002
- McKay, M.D. Beckman, R.J. Conover, W.J. “A Comparison of Three Methods for Selecting Values of Input Variables in the Analysis of Output from a Computer Code” Technometrics 21 1 239 245 1979
- McRae, G. “New Directions in Model Based Data Assimilation” MIT Chemical Engineering course 10 2000
- Nayfeh, A.H. Perturbation Methods Wiely-Interscience London 1973
- Nayfeh, A.H. Introduction to Perturbation Techniques Wiely-Interscience London 1981
- Roberts, J.B. Spanos, P.D. “Stochastic Averaging: An Approximate Method of Solving Random Vibration Problems,” Int. J. of Non-linear Mechanics 21 4 111 134 1986
- Roberts, J.B. Spanos, P.D. Random Vibration and Statistical Linearization John Wiley and Sons New York 1990
- Rubinstein, R.Y. Simulation and the Monte Carlo Method John Wiley New York 1981
- Soize, C. Ghanem, R. “Physical Systems with Random Uncertainties: Chaos Representations with Arbitrary Probability Measure” SIAM J. of Sci. Comp. 2003
- Spanos, P. Ghanem, R. “Boundary Element Method Analysis for Random Vibration Problems” J. of Eng. Mechanics, ASCE 117 2 409 423 Feb. 1991
- Spanos, P. Tein, W.Y. Ghanem, R. “Harmonic Analysis of Marine Risers with Time-Dependent Tension” Applied Ocean Research 12 4 200 211 Dec. 1990
- Spanos, P. Ghanem, R. “Stochastic Finite Element Expansion for Random Media” J. of Eng. Mechanics , ASCE 115 5 1035 1053 May 1989
- Spanos, P.D. Donley, M.G. “Equivalent statistical quadratization for nonlinear systems” J.of Engineering Mechanics 117 6 1289 1310 1991
- Spanos, P.D. Mignolet, M.D. “Arma Monte Carlo Simulation in Probabilistic Structural Analysis” Shock and Vibration Digest 21 3 10 1989
- Stolarski, R.S. “Uncertainty and sensitivity studies of stratospheric photochemistry” Proc. of the NATO Advanced Study Institute on Atmospheric Ozone: Its Variations and Human Influences Aikin A.C. 865 876 U.S. Dep. Of Transp. Washington D.C. 1980
- Stratonovich, R.L. Topics in the Theory of Random Noise Gordon and Breach New York 1963
- Tatang, M.A. Pan, W. Prinn, R.G. McRae, G.J. “An efficient method for parametric uncertainty analysis of numerical geophysical models” J. Geophy. Res. 102 21925 21932 1997
- Trefethen, L.N. Baw, D., III “Spectral Methods in MATLAB” SIAM 1998
- Van de Wouw, N. Nijmeijer, H. van Campen, D.H. “A Volterra Series Approach to the Approximation of Stochastic Nonlinear Dynamics.” Nonlinear Dynamics 27 397 409 2002
- Wu, W.F. Lin, Y.K. “Cumulant-neglect Closure for Non-linear Oscillators under Random Parametric and External Excitation,” Int. J. of Non-linear Mechanics 19 4 349 362 1984
- Xiu, D. Karniadakis, G.E. “On the Well-Posedness of Generalized Polynomial Chaos Expansions for the Stochastic Diffusion Equation” SIAM J. on Numerical Analysis 2003
- Xiu, D. Karniadakis, G.E. “A New Stochastic Approach to Transient Heat Conduction Modeling with Uncertainty” Int. J. of Heat and Mass Transfer 46 4681 4693 2003
- Xiu, D. Karniadakis, G.E. “Uncertainty Modeling of Burgers Equation by Generalized Polynomial Chaos” Computational Stochastic Mechanics, Proc. of the 4th Int. Conf. on Computational Stochastic Mechanics Corfu, Greece June 2002 Spanos P.D. Deodatis G. 655 661 Millpress Rotterdam 2003
- Xiu, D. Karniadakis, G.E. “Modeling Uncertainty in Flow Simulations via Generalized Polynomial Chaos” J. Comp. Phys. 187 137 167 2003
- Xiu, D. Karniadakis, G.E. “The Wiener-Askey Polynomial Chaos for Stochastic Differential Equations” SIAM J. Sci. Comput. 24 1 619 644 2002
- Xiu, D. Karniadakis, G.E. “Modeling Uncertainty in Steady State Diffusion Problems via Generalized Polynomial Chaos” Comput. Meth. Appl. Mech. Eng. 191 4927 4948 2002
- Xiu, D. Lucor, D. Su, C.-H. Karniadakis, G.E. “Stochastic Modeling of Flow-Structure Interactions using Generalized Polynomial Chaos” J. Fluids Engineering 124 51 59 2002
- Xiu, D. Karniadakis, G.E. “Supersensitivity due to Uncertain Boundary Conditions” Int. J. for Numerical Methods in Engineering 2003
- Zhu, W.Q. “Stochastic Averaging Methods in Random Vibration,” Applied Mechanics Review 41 5 189 199 1988