 | | Mechanics of Solids
A Journal of Russian Academy of Sciences | | Founded
in January 1966
Issued 6 times a year
Print ISSN 0025-6544
Online ISSN 1934-7936 |
Archive of Issues
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| In English (Mech. Solids): | | 3212 |
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| A. S. Gorobtsov, "Analysis of impact interactions in dynamics of many-body mechanical systems," Mech. Solids. 42 (4), 546-551 (2007) |
| Year |
2007 |
Volume |
42 |
Number |
4 |
Pages |
546-551 |
| Title |
Analysis of impact interactions in dynamics of many-body mechanical systems |
| Author(s) |
A. S. Gorobtsov (Institute for Precision Mechanics and Control Problems, Rabochaya 24, Saratov, 410028, Russia, gorobtsov@avtlg.ru) |
| Abstract |
Nowadays, methods for representing the dynamic equations of coupled systems of bodies in a form suitable for numerical solution are used widely. On the basis of such approaches, universal software aimed at solving certain classes of problems is developed [1–3].
In design diagrams of mechanical systems, it is necessary to take into account various nonlinearities, including those of impact type. The representation of impact interactions with the use of nonlinear characteristics of positional forces results in increased stiffness of the system of differential equations and increased time expenditures for the solution, because it is necessary to decrease the integration step or use implicit integration methods.
In this connection, it is expedient to consider approaches based on assumptions of the impact theory, i.e., the assumptions that the time of impact interaction is negligibly small and the impact is absolutely inelastic or partially elastic.
In the general statement, an impact in a system with arbitrarily many stationary and impact constraints was studied in [4], where a special term-system impact-was introduced to denote this problem, showing that the constant and discontinuous constraints are multidimensional.
In the present paper, we give a method for the numerical implementation of the methods proposed in [4] with the use of the FRUND software designed for modeling the dynamics of systems of rigid and elastic bodies [2]. We analyze the efficiency of their application.
According to [4], the system impact problem is stated as follows. For a many-body mechanical system with arbitrary kinematic constraints, it is required to determine the impact discontinuity of velocities as the number of constraints varies instantaneously. |
| References |
| 1. | G. B. Efimov and D. Yu. Pogorelov,
"Universal Mechanism" - a Complex of Programs for Modeling the Dynamics
of Systems of Solid Bodies,"
Preprint No. 77, IPM RAN
(Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, Moscow, 1993)
[in Russian]. |
| 2. | S. A. Kurdyuk and E. N. Shmelev,
"Specifics of Constructing Mathematical Models of
Engineering Objects Using. the Software Package RRADIS,"
Inform. Tekhnologii, No. 3, 14-19 (1996). |
| 3. | A. S. Gorobtsov and S. K. Kartsov, "Experience of Computer
Modeling of Transport Construction Vibrations," in Proceedings of the 5th International Conference on Vibration
Problems "ICOP-2001" (Moscow, 2001), pp. 186-190 [in Russian]. |
| 4. | V. V. Velichenko, "System Impact in Vibrations of Compound
Mechanical Systems," in Proceedings of the 5th International
Conference on Vibration Problems "ICOP-2001" (Moscow, 2001),
pp. 142-145 [in Russian]. |
| 5. | V. V. Velichenko, Matrix-Geometrical Methods in Mechanics with
Application to Problems of Robotics (Nauka, Moscow,
1988) [in Russian]. |
| 6. | E. Bayo and M. A. Serna, "Penalty Formulations for the Dynamics
Analysis of Elastic Mechanisms," Trans. ASME J. Mech. Transmiss.
and Autom. Des. 111 (3), 321-327 (1989). |
| 7. | A. S. Gorobtsov, "Numerical Integration of Equations of Motion for
Systems of Bodies of Arbitrary Structure," in Problems and
Perspectives of Precession Mechanics and Control in Machine
Construction. Materials of the International Conference (Saratov,
2002), pp. 16-20 [in Russian]. |
|
| Received |
22 January 2004 |
| Link to Fulltext |
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