Abstract
A model is presented for the impact with friction of a flexible body in translation and rotation. This model consists of a system of nonlinear differential equations which considers the multiple collisions as well as frictional effects at the contacting end, and allows one to predict the rigid and elastic body motion after the impact. The kinetic energy is derived by utilizing a generalized velocity field theory for elastic solids. The model uses a dry coefficient of friction and a nonlinear contact force. We introduce a finite number of vibrational modes to take into account the vibrational behavior of the body during impact. The vibrations, the multiple collisions, and the angle of incidence angle, are found to be important factors for the kinematics of frictional impact. Analytical and experimental results were compared to establish the accuracy of the model.
Similar content being viewed by others
References
Morin A., Notions fondamentales de mécanique, Hachette, Paris, 1855.
Newton I., Philosophiae naturalis principia mathematica, Reg. Soc. Praeses, London, 1686.
Poisson S. D., Mechanics, Longmans, London, 1817.
Stronge W. J., ‘Rigid body collisions with friction’, Proceedings of Royal Society, A 431 1990, 169–181.
Han I. and Gilmore B. J., ‘Multi-body impact motion with friction-analysis, simulation, and experimental validation’, ASME Journal of Mechanical Design 115, 1993, 412–422.
Hurmuzlu Y. and Marghitu D. B., ‘Rigid body collisions of planar kinematic chains with multiple contact points’, The International Journal of Robotics Research 13 (1) 1994, 82–92.
Marghitu, D. B. and Hurmuzlu, Y., ‘Three dimensional rigid body collisions with multiple contact points’, to appear in ASME Journal of Applied Mechanics, 1995.
Love A. E. H., A Treatise on the Mathematical Theory of Elasticity, Dover, New York, 1944.
Gau W. H. and Shabana A. A., ‘Use of the generalized impulse momentum equations in analysis of wave propagation’, ASME Journal of Vibration and Acoustics 113, 1991, 532–542.
Gau W. H. and Shabana A. A., ‘Effect of a finite rotation on the propagation of elastic waves in constrained mechanical systems’, ASME Journal of Mechanical Design 114 1992, 384–393.
Shabana A. A. and Gau W. H., ‘Propagation of impact-induced longitudinal waves in mechanical systems with variable kinematic structure’, Journal of Sound and Vibration 115, 1993, 1–8.
Yigit A. S., Ulsoy A. G., and Scott R. A., ‘Dynamics of a radially rotating beam with impact, Part 2: Experimental and simulation results’, ASME Journal of Vibration and Acoustics 112, 1990, 71–77.
Yigit A. S., Ulsoy A. G. and Scott R. A., ‘Spring-dashpot models for the dynamics of a radially rotating beam with impact’, Journal of Sound and Vibration 142, 1990 515–525.
Mason H. L., ‘Impact of beams’, Transactions of the ASME 58, 1935, A55-A61.
Goldsmith W., Impaet, Edward Arnold Publishers Ltd., London, U.K., 1960.
Stolanovici, D. and Hurmuzlu, Y., ‘A critical study of the concepts of rigid body collision theory’, to appear in ASME Journal of Applied Mechanics, 1995.
Kane T. R., Ryan R. R., and Banerjee A. K., ‘Dynamics of a cantilever beam attached to a moving base’, Journal of Guidance, Control, and Dynamics 10 (2), 1987, 139–151.
Brach R. M., Mechanical Impact Dynamics, John Wiley & Sons, New York, 1991.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Marghitu, D.B., Hurmuzlu, Y. Nonlinear dynamics of an elastic rod with frictional impact. Nonlinear Dyn 10, 187–201 (1996). https://doi.org/10.1007/BF00045457
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF00045457