Abstract
In the present paper, it is shown how one can employ existing rigid body codes to handle systems containing elastic plates by using a Rayleigh–Ritz discretization procedure. The equations of motion are formulated for a rectangular plate undergoing large rigid body motions but small elastic deformations. Geometric nonlinearities in the elastic coordinates are taken into account to include the effect of dynamic stiffening. As an example, a spin-up maneuver for a simply-supported plate is treated.
Similar content being viewed by others
References
Banerjee, A.K. and Kane, T.R., 'Dynamics of a plate in large overall motion' Journal of Applied Mechanics 56, 1989, 887–892.
Botz, M. and Hagedorn, P., 'Multiple body systems with flexiblemembers', Nonlinear Dynamics 1, 1990, 433–447.
Botz, M. and Hagedorn, P., 'Dynamic simulation of elastic multibody systems using existing rigid body codes', in Proc. 2nd ESA Workshop: Modal Representation of Flexible Structures by Continuum Methods, ESA WPP034, 1992, 265–275.
Botz, M. and Hagedorn, P., 'On the dynamics of multibody systems with elastic beams', in Advanced Multibody System Dynamics – Simulation and Software Tools, W.O. Schiehlen (ed.), Kluwer Academic Publishers, Dordrecht, 1993, 217–236.
Huston, R.L. and Wang, Y., 'Flexibility effects in multibody systemsx', in Computer Aided Analysis of Rigid and Flexible Mechanical Systems, M.F.O.S. Pereira and J.A.C. Ambrosio (eds), Kluwer Academic Publishers, Dordrecht, 1994, 351–376.
Kane, T.R. and Levinson, D.A., Dynamics: Theory and Applications, McGraw-Hill, New York, 1985.
Kane, T.R. and Ryan, R.R. and Banerjee, A.K., 'Dynamics of a cantilever beam attached to a moving base', Journal of Guidance Control and Dynamics 10, 1987, pp. 139–151.
Schaechter, D.B. and Levinson, D.A. and Kane, T.R., Autolev User's Manual, OnLine Dynamics, Inc., Sunnyvale, 1988.
Rauh, J., 'Ein Beitrag zur Modellierung elastischer Balkensysteme', VDI-FortschrittBerichte, Reihe 18, Nr. 37, VDI-Verlag, Düsseldorf, 1987.
Shabana, A.A., Dynamics of Multibody Systems, Wiley, New York, 1989.
Timoshenko, S.P. and Woinowsky-Krieger, S., Theory of Plates and Shells, McGraw-Hill, New York, 1959.
Valembois, R.E. and Fisette, P. and Samin, J.C., 'Comparison of various techniques for modelling flexible beams in multibody dynamics', Nonlinear Dynamics 12, 1997, 367–397.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Hagedorn, P., Botz, M. Elastic Plates in Multibody Systems: A Treatment Using Existing Rigid Body Codes. Multibody System Dynamics 1, 351–359 (1997). https://doi.org/10.1023/A:1009737121336
Issue Date:
DOI: https://doi.org/10.1023/A:1009737121336