Abstract
In this paper several formulations for automatic generation of the equations of motion for rigid and flexible multibody systems are reviewed. These formulations are of special interest for vehicle dynamics and crash analysis. We first discuss a so-called body-coordinate formulation to construct the Newton-Euler equations of motion for constrained rigid multibody systems. Then we review a nonconventional point-coordinate formulation. An easy-to-use method for deriving the equations of motion for flexible bodies in a multibody environment is also presented. Several ideas on how a body-fixed frame can be attached to a flexible body are discussed. It is shown how these formulations for rigid and flexible bodies could be mixed in order to construct the complete set of equations of motion. The constructed equations are normally a large set of mixed differential-algebraic equations. The method of joint-coordinates for transforming these equations to a smaller set is briefly discussed. Two application examples for ride/handling and crash analyses are also presented.
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References
Nikravesh, P.E. (1988) Computer-Aided Analysis of Mechanical Systems, Prentice-Hall.
Garcia de Jalon, J. And Bayo, E. (1994) Kinematic and Dynamic Simulations of Multibody Systems, Springer-Verlag.
Nikravesh, P.E. and Affifi, H.A. (1994) Construction of the Equations of Motion for Multibody Dynamics Using Point and Joint Coordinates, Computer-Aided Analysis of Rigid and Flexible Mechanical Systems, Kluwer academic publishers, NATO ASI Series E: Applied Sciences — Vol. 268, pp.31–60.
Agrawal, O.P. and Shabana, A.A. (1986) Application of Deformable-Body Mean Axis to Flexible Multibody System Dynamics, Computer Methods in Applied Mechanics and Engineering 56, 217–245.
Jerkovsky, W. (1978) The Structure of Multibody Dynamics Equations, J. Guidance and Control, Vol. 1, No. 3, pp. 173–182.
Kim, S.S. and Vanderploeg, M.J. (1986) A General and Efficient Method for Dynamic Analysis of Mechanical Systems Using Velocity Transformation, ASME J. Mech., Trans., and Auto. In Design, Vol. 108, 176–182.
Nikravesh, P.E. and Gim, G. (1993) Systematic Construction of the Equations of Motion for Multibody Systems Containing Closed Kinematic Loops, ASME J. Of Mechanical Design, Vol. 115, No. 1, 143–149.
Bakker, E., Nyborg, L. And Pacjeks, H.B. (1987) Tyre Modeling for Use in Vehicle Dynamics Studies, SAE paper, No. 870421.
Park, J. And Nikravesh, P.E. (1997) A Multibody Approach to Modeling Tire Longitudinal/Lateral Flexibility, February 1997 SAE International Congress and Exposition.
Ambrósio, J.A.C. (1991) Elastic-Plastic Large Deformation of Flexible Multibody Systems in Crash Analysis, Ph.D. Dissertation, University of Arizona, Tucson, AZ.
Nikravesh, P.E. and Ambrósio, J. A.C. ( 1991 ) Systematic Construction of the Equations of Motion for Rigid-Flexible Multibody Systems Containing Open and Closed Kinematic Loops, Int. J. Of Num. Meth. In Eng., Vol. 32, 1749–1766.
Ambrósio, J.A.C. and Nikravesh, P.E. (1992) Elasto-Plastic Deformation in Multibody Dynamics, Nonlinear Dynamics, Vol. 3, 85–104.
Nikravesh, P.E. and Chung, I.S. (1984) Structural Collapse and Vehicular Crash Simulation Using a Plastic Hinge Technique, J. Struct. Mech., 12(3), 371–400.
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© 1997 Springer Science+Business Media Dordrecht
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Nikravesh, P.E. (1997). Rigid-Flexible Multibody Equations of Motion Suitable for Vehicle Dynamics and Crash Analysis. In: Ambrósio, J.A.C., Pereira, M.F.O.S., da Silva, F.P. (eds) Crashworthiness of Transportation Systems: Structural Impact and Occupant Protection. NATO ASI Series, vol 332. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-5796-4_17
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DOI: https://doi.org/10.1007/978-94-011-5796-4_17
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