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Comparison of natural complement formulations for multibody dynamics

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Języki publikacji
EN
Abstrakty
EN
The main aim of this paper is to compare the effectiveness of numerical techniques used for spatial multibody dynamics simulation by applying the natural complement method. In the paper, seven numerical schemes are considered: zero eigenvalue formulation, Pseudo Upper Triangular Decomposition, Schur decomposition, Singular Value Decomposition, QR decomposition, coordinate partitioning and Wang-Huston formulation. In order to illustrate the effectiveness of these schemes, two McPherson struts are considered. Simulations are performed with four error tolerance values and for three stabilization cases. Some suggestions on possible applications of the selected methods are formulated.
Rocznik
Strony
1391--1404
Opis fizyczny
Bibliogr. 32 poz., rys., tab.
Twórcy
autor
  • Warsaw University of Technology, Institute of Aeronautics and Applied Mechanics, Poland
autor
  • Warsaw University of Technology, Institute of Aeronautics and Applied Mechanics, Poland
Bibliografia
  • 1. Amirouche F.M.L., 2006, Fundamentals of Multibody Dynamics, Theory and Applications, Birkh¨auser Boston
  • 2. Awrejcewicz J., 2014, Ordinary Differential Equations and Mechanical Systems, Springer International Publishing
  • 3. Awrejcewicz J., Kudra G., 2005, Modeling, numerical analysis and application of triple physical pendulum with rigid limiters of motion, Archive of Applied Mechanics, 74, 11-12, 746-753
  • 4. Awrejcewicz J., Kudra G., 2014, Mathematical modelling and simulation of the bifurcational wobblestone dynamics, Discontinuity, Nonlinearity, and Complexity, 3, 2, 123-132
  • 5. Awrejcewicz J., Kudra G., Lamarque C.H., 2003, Dynamics investigation of three coupled rods with a horizontal barrier, Meccanica, 38, 6, 687-698
  • 6. Awrejcewicz J., Kudra G., Lamarque C.H., 2004, Investigation of triple pendulum with impacts using fundamental solution matrices, International Journal of Bifurcation and Chaos, 14, 12, 4191-4213
  • 7. Baumgarte J.W., 1972, Stabilization of constraints and integrals of motion in dynamical systems, Computer Methods in Applied Mechanics and Engineering, 1, 1, 1-16
  • 8. de Jalón J.G., Bayo E., 1994, Kinematic and Dynamic Simulation of Multibody Systems, The Real-Time Challenge, Springer-Verlag, New-York
  • 9. de Jalón J.G., Guti´errez-López M.D., 2013, Multibody dynamics with redundant constraints and singular mass matrix: existence, uniqueness, and determination of solutions for accelerations and constraint forces, Multibody System Dynamics, 30, 3, 311-341
  • 10. Eich-Soellner E., Fuhrer C. ¨ , 1998, Numerical Methods in Multibody Dynamics, B.G. Teubner
  • 11. Frączek J., Wojtyra M., 2008, Kinematyka układów wieloczłonowych. Metody obliczeniowe, Wydawnictwa Naukowo-Techniczne, Warszawa
  • 12. FreeMat v4.1, help 1
  • 3. Golub G.H., Loan C.F.V., 1996, Matrix Computations, The Johns Hopkins University Press, 3rd edition
  • 14. Hartfiel D.J., 2001, Matrix Theory and Applications with MATLAB, CRC Press
  • 15. Haug E.J., 1989, Computer Aided Kinematics and Dynamics of Mechanical Systems, Vol. I: Basic Methods, Allyn and Bacon
  • 16. Ider S.K., Amirouche F.M.L., 1988, Coordinate reduction in the dynamics of constrained multibody systems – a new approach, ASME Journal of Applied Mechanics, 55, 4, 899-904
  • 17. Kim S.S., Vanderploeg M.J., 1986, QR decomposition for state space representation of constrained mechanical dynamic systems, ASME Journal of Mechanisms, Transmissions, and Automation in Design, 108, 2, 183-188
  • 18. Kincaid D., Cheney W., 2002, Numerical Analysis: Mathematics of Scientific Computing, Brooks/Cole, 3-rd edition
  • 19. Kunkel P., Mehrman V., 2006, Differential-Algebraic Equations, European Mathematical Society
  • 20. Malczyk P., Frączek J., 2012, A divide and conquer algorithm for constrained multibody system dynamics based on augmented Lagrangian method with projections-based error correction, Nonlinear Dynamics, 70, 1, 871-889
  • 21. Mani N.K., Haug E.J., Atkinson K.E., 1985, Application of singular value decomposition for analysis of mechanical system dynamics, ASME Journal of Mechanisms, Transmissions, and Automation in Design, 107, 1, 82-87
  • 22. Mariti L., Belfiore N.P., Pennestr`ı E., Valentini P.P., 2011, Comparison of solution strategies for multibody dynamics equations, International Journal for Numerical Methods in Engineering, 88, 7, 637-656
  • 23. Mariti L., Pennestr`ı E., Valentini P.P., Belfiore N.P., 2010, Review and comparison of solution strategies for multibody dynamics equations, The 1st Joint International Conference on Multibody System Dynamics, Lappeenranta, Finland
  • 24. MATLAB®, help
  • 25. Negrut D., Serban R., Potra F.A., 1997, A topology-based approach to exploiting sparsity in multibody dynamics: joint formulation, Mechanics of Structures and Machines, 25, 2, 221-241
  • 26. Ostalczyk P., 2008, Wybrane zagadnienia rachunku wektorowego i macierzowego dla robotyków, Wydawnictwo Politechniki Łódzkiej, Łódź
  • 27. Pennestr`ı , Valentini P.P., 2007, Coordinate reduction strategies in multibody dynamics: A review, Proceedings of the Conference on Multibody System Dynamics
  • 28. Pękal M., 2012, Porównanie metod całkowania RRA w analizie dynamiki układów wieloczłonowych (in Polish), praca dyplomowa magisterska, Politechnika Warszawska, Warszawa
  • 29. Walton W.C., Steeves E.C., 1969, A New Matrix Theorem and Its Application for Establishing Independent Coordinates for Complex Dynamical Systems with Constraints, NASA Technical Report: NASA TR R-326, NASA, Washington D. C.
  • 30. Wang J.T., Huston R.L., 1989, A comparison of analysis methods of redundant multibody systems, Mechanics Research Communications, 16, 3, 175-182
  • 31. Wehage R.A., Haug E.J., 1982, Generalized coordinate partitioning for dimension reduction in analysis of constrained dynamic systems, ASME Journal of Mechanical Design, 104, 1, 247-255
  • 32. Wojtyra M., Frączek J., 2013, Comparison of selected methods of handling redundant constraints in multibody systems simulations, Journal of Computational and Nonlinear Dynamics, 8, 2, 021007 (1-9)
Uwagi
PL
Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniajacą naukę.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-a1593d73-50fd-4233-9827-6b9cd4aa7431
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