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Modeling multibody systems with uncertainties. Part II: Numerical applications

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Abstract

This study applies generalized polynomial chaos theory to model complex nonlinear multibody dynamic systems operating in the presence of parametric and external uncertainty. Theoretical and computational aspects of this methodology are discussed in the companion paper “Modeling Multibody Dynamic Systems With Uncertainties. Part I: Theoretical and Computational Aspects”.

In this paper we illustrate the methodology on selected test cases. The combined effects of parametric and forcing uncertainties are studied for a quarter car model. The uncertainty distributions in the system response in both time and frequency domains are validated against Monte-Carlo simulations. Results indicate that polynomial chaos is more efficient than Monte Carlo and more accurate than statistical linearization. The results of the direct collocation approach are similar to the ones obtained with the Galerkin approach. A stochastic terrain model is constructed using a truncated Karhunen-Loeve expansion. The application of polynomial chaos to differential-algebraic systems is illustrated using the constrained pendulum problem. Limitations of the polynomial chaos approach are studied on two different test problems, one with multiple attractor points, and the second with a chaotic evolution and a nonlinear attractor set.

The overall conclusion is that, despite its limitations, generalized polynomial chaos is a powerful approach for the simulation of multibody dynamic systems with uncertainties.

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Authors and Affiliations

  1. Mechanical Engineering Department, Virginia Polytechnic Institute and State University, Blacksburg, Virginia, United States

    Corina Sandu & Mehdi Ahmadian

  2. Mechanical Engineering Department, Virginia Polytechnic Institute and State University, 101 Randolph Hall Virginia Tech, Blacksburg, VA, 24061, USA

    Adrian Sandu

Authors
  1. Corina Sandu
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  2. Adrian Sandu
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  3. Mehdi Ahmadian
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Correspondence to Corina Sandu.

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Sandu, C., Sandu, A. & Ahmadian, M. Modeling multibody systems with uncertainties. Part II: Numerical applications. Multibody Syst Dyn 15, 241–262 (2006). https://doi.org/10.1007/s11044-006-9008-4

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  • DOI: https://doi.org/10.1007/s11044-006-9008-4

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