SIMULTANEOUS MULTI – COLLISION OF A RIGID BODY WITHOUT FRICTION

Nicolae-Doru STĂNESCU, Nicolae PANDREA

Abstract


 In our paper we discuss the collision without friction of a rigid body with many obstacles at the same time. The problem is solved using the notion of inertance. We deduced the expressions of the impulse at any contact point, distribution of velocities after the collision, energy of lost velocities and variation of kinetic energy. The obtained formulae are general and written in matrix form. An example highlights the theory.

Key words: multi-collision, simultaneous, inertance, coefficients of restitution, impulse, velocities, energy of lost velocities, variation of kinetic energy.


Full Text:

PDF

References


Batlle, J., A., Termination condition for three-dimensional inelastic collisions in multibody systems, International Journal of Impact Engineering 2001; 25: 615-629.

Batlle, J., A., Cardona, S., The jamb (self locking) process in three-dimensional collisions, ASME Journal of Applied Mechanics 1998; 65(2): 417-423.

Brach, R., M., Friction restitution and energy loss in planar collision, ASME Journal of Applied Mechanics 1984; 51(1): 164-170. DOI: 10.1115/1.3167562.

Brach, R., M., Rigid body collision, ASME Journal of Applied Mechanics 1989; 56(1): 133-138. DOI: 10.1115/1.3176033

Brogliato, B., Kinetic quasi-velocities in unilaterally constrained Lagrangian mechanics with impacts and friction, Multibody System Dynamics 2014; 32: 175-216. DOI: 10.1007/s11044-013-9392-5.

Brogliato, B., Nonsmooth Mechanics, 3rd ed. Berlin: Springer, 2016.

Dimentberg, F., The theory of screws and its applications. Moskow: Nauka, 1978.

Elkaranshawy, H., A., Rough collision in three-dimensional rigid multi-body systems, Proceedings of the Institution of Mechanical Engineers, Part K: Journal of Multi-body Dynamics 2007; 221(4): 541-550. DOI: 10.1243/14644193JMBD99.

Flores, P., Ambrósio, J., Claro, J., C., P., Lankarani, H., M., Influence of the contact-impact force model on the dynamic response of multi-body systems, Proceedings of the Institution of Mechanical Engineers, Part K: Journal of Multi-body Dynamics 2006; 220 (1): 21-34. DOI: 10.1243/146441906X77722.

Glocker, C., Energetic consistency conditions for standard impacts. Part I: Newton-type inequality impact laws, Multibody System Dynamics 2013; 29:77-117, 2013. DOI: 10.1007/s11044-012-9316-9.

Glocker, C., Energetic consistency conditions for standard impacts. Part II: Poisson-type inequality impact laws, Multibody System Dynamics 2014; 32: 445-509. DOI: 10.1007/s11044-013-9387-2.

Kapoulitsas, M., G., On the collision of rigid bodies, Journal of Applied Mathematics and Physics (ZAMP) 1995; 46: 709-723.

Keller, J., B., Impact with friction, ASME Journal of Applied Mechanics 1986; 53(1): 1-4. DOI: 10.1115/1.3171712.

Lankarani, H., M., Pereira, M., F., O., S., Treatment of impact with friction in planar multibody mechanical systems, Multibody System Dynamics 2001; 6(3): 203-227.

Marghitu, B., D., Hurmuzlu, Y., Three-dimensional rigid body collisions with multiple contact points, ASME Journal of Applied Mechanics 1995; 62(3): 725-732. DOI: 10.1115/1.2897006.

Pandrea, N., On the collisions of solids, Studies and researches of Applied Mechanics 1990; 40(2): 117-131.

Pandrea, N., Elements of the mechanics of solid rigid in plückerian coordinates, Bucharest: The Publishing House of the Romanian Academy, 2000.

Pandrea, N., About collisions of two solids with constraints, Revue Romaine des Sciences Techniques, série de Méchanique Appliquée 2004; 49(1): 1-6.

Pandrea, N., Stănescu, N.-D., A New Approach in the Study of Frictionless Collisions Using Inertances, Proceedings of the International Institution of Mechanical Engineers, Part C, Journal of Mechanical Engineering Science, 2015, 229(12): 2144–2157, DOI: 10.1177/0954406214553983.

Pandrea, N., Stănescu, N.-D., A New Approach in the Study of the Collisions with Friction Using Inertances, Proceedings of the International Institution of Mechanical Engineers, Part C, Journal of Mechanical Engineering Science (in press).

Pandrea, N., Stănescu, N.-D., Dynamics of the Rigid Solid with General Constraints by a Multibody Approach, John Wiley & Sons, Chichester, UK, 2016.

Pennestri, E., Valentini, P., P., Vita, L., Dynamic Analysis of Intermitent-Motion Mechanisms Through the Combined Use of Gauss Principle and Logical Functions, IUTAM Symposium on Multiscale Problems in Multibody System Contacts Stuttgart February 2006;Springer-Verlag, IUITAM Book series, ISBN 976-1-4020-5980-3; 2006: 195-204.

Pfeiffer, F., On impact with friction, Applied Mathematics and Computation 2010; 217(3): 1184-1192. DOI: 10.1016/j.amc.2010.05.047.

Stănescu, N.-D., Munteanu, L, Chiroiu, V., Pandrea, N., Dynamical systems. Theory and applications. Bucharest: The Publishing House of the Romanian Academy, 2007.

Stronge, J.,W., Rigid body collision with friction, Proceedings of the Royal Society, A, Mathematical, Physical & Engineering Sciences 1990; 431(1881): 169-181. DOI: 10.1098/rspa.1990.0125

Stronge, J., W., Impact Mechanics. Cambridge: Cambridge University Press, 2000.

Tavakoli, A., Gharib, M., Hurmuzlu, Y., Collision of two mass batons with massive external surfaces, ASME Journal of Applied Mechanics 2012; 79(5): 051019 1-8. DOI: 10.1115/1.4006456.

Voinea, R., Pandrea, N., Contribution to a general mathematical theory of kinematic linkages, Proc. IFTOMM International Symposium on Linkages and Computer Design Method B, 1973, pp. 522-534. Bucharest.

Wang, Y., Mason, T., M., Two-dimensional rigid-body collisions with friction, ASME Journal of Applied Mechanics 1992; 59(3): 635-642. DOI: 10.1115/1.2893771.

Yao, W., Chen, B., Liu, C., Energetic coefficient of restitution for planar impact in multi-rigid-body systems with friction, International Journal of Impact Engineering 2005; 31(3): 255-265.

Woo, L., Freudenstein, F., Application of line geometry to theoretical kinematics and the kinematic analysis of mechanical systems, Journal of Mechanisms 1970; 5(3): 417-460.

Yu, H.-N., Zhao, J.-S., Chu, F.-L., An enhanced multi-point dynamics methodology for collision and contact problems, Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 2013; 227(6): 1203-1223. DOI: 10.1177/0954406212460973.

Yuan, M., Freudenstein, F., Kinematic analysis of spatial mechanisms by means of screw coordinates, ASME Journal of Engineering for Industry 1973; 93(1): 61-73.


Refbacks

  • There are currently no refbacks.


JOURNAL INDEXED IN :