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Abstract
The modelling of flexible elements in mechanical systems has been widely investigated through several methods issuing from both the area of structural mechanics and the field of multibody dynamics. As regards the latter discipline, beside the problem of the generation of the multibody equations of motion, the choice of a spatial discretization method for modelling flexible elements has always been considered as a critical phase of the modelling. Although this subject is abundantly tackled in the open-literature, the latter probably lacks an objective comparison between the most commonly used approaches.
This contribution presents an extensive investigation of several discretization techniques of flexible beams, in a pure multibody context. In particular, it is shown that shape functions based on power series monomials are very suitable and versatile to model beams being part of a multibody system and thus constitutes an interesting alternative to finite element analysis. For this purpose, a symbolic multibody program, in which various discretization techniques were implemented, was generalized to compute the equations of motion of a general multibody system containing flexible beams.
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References
Meirovitch, L. and Kwak, M. K., ‘Rayleigh-Ritz based substructure synthesis for flexible multibody systems’,American Institute of Aeronautics and Astronautics Journal28, 1991, 1709–1719.
Kane, T. R., Ryan, P. R., and Banerjee, A. K., ‘Dynamics of a cantilever beam attached to a moving base’,Journal of Guidance, Control, and Dynamics10, 1987, 139–151.
Wallrapp, O. and Schwertassek, R., ‘Representation of geometric stiffening in multibody system simulation’,International Journal of Numerical Methods in Engineering32, 1991, 1833–1850.
Jen, C. W., Johnson, D. A., and Dubois, F., ‘Numerical modal analysis of structures based on a revised substructure synthesis approach’,Journal of Sound and Vibration180(2), 1995, 185–203.
Fisette, P., Johnson, D. A., and Samin J. C., ‘A fully symbolic generation of the equations of motion of multibody systems containing flexible beams’,Computer Methods in Applied Mechanics and Engineering (to appear).
G00E9rardin, M., Cardona, A., Doan, D. B., and Duysens, J., ‘Finite elements modeling concepts in multibody dynamics’, inComputer-Aided Analysis of Rigid and Flexible Mechanical Systems, M. Pereira and J. Ambrosio (eds.), NATO ASI Series, Applied Sciences, Vol. 268, Kluwer, Dordrecht, 1993, pp. 233–284.
Huston, R. L. and Wang, Y., ‘Flexibility effects in multibody systems’, inComputer-Aided Analysis of Rigid and Flexible Mechanical Systems, M. Pereira and J. Ambrosio (eds.), NATO ASI Series, Applied Sciences, Vol. 268, Kluwer, Dordrecht, 1993, pp. 351–376.
Maes, P., Samin, J.C., and Willems, P. Y., ‘Robotran’, inMultibody System Handbook, W. Schiehlen (ed.), Springer-Verlag, Berlin, 1989, pp. 225–245.
‘Module d' Analyse de M00E9canismes Flexibles MECANO: Manuel d' utilisation’, SAMTECH S.A., Li00E8ge, Belgium, 1994.
G00E9rardin, M. and Cardona, A., ‘A beam finite element non-linear theory with finite rotations’,International Journal of Numerical Methods in Engineering26, 1988, 2403–2438.
Fisette, P., ‘G00E9n00E9ration symbolique des 00E9quations du mouvement de syst00E8mes multicorps et application dans le domaine ferroviaire’, Ph.D. Thesis, UCL, Louvain-la-Neuve, Belgium 1994.
Fisette, P. and Samin, J. C., ‘Symbolic generation of large multibody system dynamic equations using a new semi-explicit Newton/Euler recursive scheme’,Archives of Applied Mechanics66, 1996, 187–199.
Renaud, M., ‘Quasi-minimal computation of the dynamic model of a robot manipulator utilizing the Newton- Euler formalism and the notion of augmented body’, inProceedings of the IEEE International Conference on Robotics and Automation, Rayleigh, North Carolina, 1987, pp. 1677–1682.
Willems, P. Y.,Introduction 00E0 la M00E9canique, Masson, Paris, 1979.
Hairer, E. and Wanner, G., ‘Solving ordinary differential equations II. Stiff and differential-algebraic problems’, in Springer Series in Computational Mathematics, Vol. 14, Springer-Verlag, 1991.
Leung, A. Y. T., ‘Fast convergence modal analysis for continuous systems’,Journal of Sound and Vibration87(3), 1983, 449–467.
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Déepartement de Méecanique, Université Catholique de Louvain, 2, Place du Levant, B-1348, Louvain-la-Neuve, Belgium
R. E. Valembois, P. Fisette & J. C. Samin
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Valembois, R.E., Fisette, P. & Samin, J.C. Comparison of Various Techniques for Modelling Flexible Beams in Multibody Dynamics.Nonlinear Dynamics12, 367–397 (1997). https://doi.org/10.1023/A:1008204330035
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