Multi-time scale simulation for impact systems: from wave propagation to rigid-body motion

Summary Impact response encompasses a variety of complicated dynamic effects including wave propagation, structural vibrations and rigid-body motion. For efficient simulation of impact response with sufficient accuracy, the methods of wave propagation and multibody systems should be combined. This paper deals with an adaptive simulation of impact response during the transition from wave propagation to rigid-body motion. For modeling structural vibrations, the approach of flexible multibody systems with floating frame of reference formulation is used and the impact-induced elastic deformations are assumed to be small. In the simulation of transient impact response, contributions of the elastic coordinates are monitored with regard to their response bounds. When response bounds are reached, the corresponding elastic coordinates are deleted. As a consequence, the number of degrees of freedom of the flexible system is reduced and the efficiency of the simulation improved. Due to material damping, the impact-induced structural vibrations decay and only the rigid-body motion remains. This adaptive simulation approach is experimentally validated for the longitudinal impact of a rigid body against an elastic rod.

[1]  S. Timoshenko,et al.  Theory of elasticity , 1975 .

[2]  W. Goldsmith,et al.  Impact: the theory and physical behaviour of colliding solids. , 1960 .

[3]  I. Szábo,et al.  Geschichte der mechanischen Prinzipien : und ihrer wichtigsten Anwendungen , 1976 .

[4]  V. Ramamurti,et al.  Impact on short length bars , 1977 .

[5]  E. Haug,et al.  Dynamic Analysis of Mechanical Systems With Intermittent Motion , 1982 .

[6]  M. M. Al-Mousawi,et al.  On Experimental Studies of Longitudinal and Flexural Wave Propagations: An Annotated Bibliography , 1986 .

[7]  Eigenvalue bounds for linear mechanical systems with nonmodal damping , 1987 .

[8]  Ahmed A. Shabana,et al.  Dynamics of Multibody Systems , 2020 .

[9]  Hamid M. Lankarani,et al.  Continuous contact force models for impact analysis in multibody systems , 1994, Nonlinear Dynamics.

[10]  Werner Schiehlen,et al.  Eigenvalue, frequency response and variance bounds of linear damped systems , 1996 .

[11]  Friedrich Pfeiffer,et al.  Multibody Dynamics with Unilateral Contacts , 1996 .

[12]  D. W. Nicholson,et al.  Stable Response of Non-Classically Damped Mechanical Systems - II , 1996 .

[13]  Ahmed A. Shabana,et al.  Flexible Multibody Dynamics: Review of Past and Recent Developments , 1997 .

[14]  Werner Schiehlen,et al.  Multibody System Dynamics: Roots and Perspectives , 1997 .

[15]  Olivier A. Bauchau,et al.  On the Modeling of Friction and Rolling in Flexible Multi-Body Systems , 1999 .

[16]  Y. Khulief.  Dynamic Response Calculation of Spatial Elastic Multibody Systems with High-Frequency Excitation , 2001 .

[17]  Peter Eberhard,et al.  Symbolic computation of longitudinal impact waves , 2001 .

[18]  Daniel J. Inman,et al.  Structural dynamics @ 2000 : current status and future directions , 2001 .

[19]  Peter Eberhard,et al.  SYMBOLICAL IMPACT ANALYSIS FOR A FALLING CONICAL ROD AGAINST THE RIGID GROUND , 2001 .

[20]  Peter Eberhard,et al.  Comparison of Analytical and Experimental Results for Longitudinal Impacts on Elastic Rods , 2003 .