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Vibrations with Collisions of a Mechanical System with Elastic Elements

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Acoustics and Vibration of Mechanical Structures—AVMS 2019

Part of the book series: Springer Proceedings in Physics ((SPPHY,volume 251))

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Abstract

In this paper, we present a mechanical system consisting in an arbitrary number of masses linked one to another by springs. The magnitudes of the vibrations are limited by some retainers located on the directions of vibrations. One knows the coefficients of restitution and the geometric and mechanical parameters of the system. The first index 0 mass is excited by a harmonic type force. We determine the equations of motion corresponding to each mass and the laws of motion, which, due to the collisions, are nonlinear ones. We also describe a numerical example for which we have drawn the diagrams of variation of the characteristic parameters.

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References

  1. J.A. Batlle, Termination condition for three-dimensional inelastic collisions in multibody systems. Int. J. Impact Eng. 25(7), 615–629 (2001)

    Article  Google Scholar 

  2. J.A. Batlle, The sliding velocity flow of rough collisions in multibody systems. ASME J. Appl. Mech. 63(3), 804–809 (1996)

    Article  ADS  Google Scholar 

  3. J.A. Batlle, S. Cardona, The jamb (self locking) process in three-dimensional collisions. ASME J. Appl. Mech. 65(2), 417–423 (1998)

    Article  ADS  Google Scholar 

  4. R.M. Brach, Friction restitution and energy loss in planar collision. ASME J. Appl. Mech. 51(1), 164–170 (1984)

    Article  ADS  Google Scholar 

  5. R.M. Brach, Rigid body collision. ASME J. Appl. Mech. 56(1), 133–138 (1989)

    Article  ADS  Google Scholar 

  6. B. Brogliato, Kinetic quasi-velocities in unilaterally constrained Lagrangian mechanics with impacts and friction. Multibody Syst. Dyn. 32, 175–216 (2014)

    Article  MathSciNet  Google Scholar 

  7. B. Brogliato, Nonsmooth Mechanics, 3rd edn. (Springer, Berlin, 2016)

    Book  Google Scholar 

  8. F. Dimentberg, The Theory of Screws and its Applications (Nauka, Moskow, 1978)

    Google Scholar 

  9. H.A. Elkaranshawy, Rough collision in three-dimensional rigid multi-body systems. Proc. Inst. Mech. Eng. Part K J. Multi-body Dyn. 221(4), 541–550 (2007)

    Google Scholar 

  10. P. Flores, J. Ambrósio, J.C.P. Claro, H.M. Lankarani, Influence of the contact-impact force model on the dynamic response of multi-body systems. Proc. Inst. Mech. Eng. Part K J. Multi-body Dyn. 220(1), 21–34 (2006)

    Google Scholar 

  11. Glocker, C.: Energetic consistency conditions for standard impacts. Part I: Newton-type inequality impact laws. Multibody System Dynamics 29, 77–117 (2013)

    Google Scholar 

  12. C. Glocker, Energetic consistency conditions for standard impacts. Part II: Poisson-type inequality impact laws. Multibody Syst. Dyn. 32, 445–509 (2014)

    Article  MathSciNet  Google Scholar 

  13. D.J. Inman, Engineering Vibration, 4th edn. (Pearson Education, New Jersey, 2013)

    Google Scholar 

  14. M.G. Kapoulitsas, On the collision of rigid bodies. J. Appl.Math. Phys. (ZAMP) 46, 709–723 (1995)

    Article  MathSciNet  Google Scholar 

  15. J.B. Keller, Impact with friction. ASME J. Appl. Mech. 53(1), 1–4 (1986)

    Article  ADS  MathSciNet  Google Scholar 

  16. H.M. Lankarani, M.F.O.S. Pereira, Treatment of impact with friction in planar multibody mechanical systems. Multibody Syst. Dyn. 6(3), 203–227 (2001)

    Article  Google Scholar 

  17. B.D. Marghitu, Y. Hurmuzlu, Three-dimensional rigid body collisions with multiple contact points. ASME J. Appl. Mech. 62(3), 725–732 (1995)

    Article  ADS  Google Scholar 

  18. L. Meirovitch, Fundamentals of Vibrations, 2nd edn. (Waveland Press, Long Grove, 2010)

    Google Scholar 

  19. N. Pandrea, On the collisions of solids. Stud. Res. Appl. Mech. 40(2), 117–131 (1990)

    Google Scholar 

  20. N. Pandrea, Elements of the Mechanics of Solid Rigid in Plückerian Coordinates (The Publishing House of the Romanian Academy, Bucharest, 2000)

    Google Scholar 

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

    Google Scholar 

  22. N. Pandrea, N.D. Stănescu, A new approach in the study of frictionless collisions using inertances. Proc. Int. Inst. Mech. Eng. Part C J. Mech. Eng. Sci. 229(12), 2144–2157 (2015)

    Article  Google Scholar 

  23. N. Pandrea, N.D. Stănescu, A new approach in the study of frictionless collisions using inertances. Proc. Int. Inst. Mech. Eng. Part C J. Mech. Eng. Sci. 233(3), 817–834 (2015)

    Article  Google Scholar 

  24. E. Pennestri, P.P. Valentini, L. Vita, Dynamic analysis of intermittent-motion mechanisms through the combined use of gauss principle and logical functions, in IUTAM Symposium on Multiscale Problems in Multibody System Contacts Stuttgart February 2006, IUITAM Book series, ed. by P. Eberhard (Springer, Heidelberg, 2006), pp. 195–204

    Google Scholar 

  25. F. Pfeiffer, On impact with friction. Appl. Math. Comput. 217(3), 1184–1192 (2010)

    MathSciNet  MATH  Google Scholar 

  26. N.D. Stănescu, L. Munteanu, V. Chiroiu, N. Pandrea, Dynamical Systems. Theory and Applications (The Publishing House of the Romanian Academy, Bucharest, 2007)

    Google Scholar 

  27. J.W. Stronge, Rigid body collision with friction. Proc. R. Soc. A Math. Phys. Eng. Sci. 431(1881), 169–181 (1990)

    ADS  MathSciNet  MATH  Google Scholar 

  28. J.W. Stronge, Impact Mechanics (Cambridge University Press, Cambridge, 2000)

    Book  Google Scholar 

  29. A. Tavakoli, M. Gharib, Y. Hurmuzlu, Collision of two mass baton with massive external surfaces. ASME J. Appl. Mech. 79(5), 051019 1–8 (2012)

    Google Scholar 

  30. S. Vlase, A method of eliminating Lagrangian multipliers from the equation of motion of interconnected mechanical systems. J. Appl. Mech. Trans. ASME 54(1), 235–237 (1987)

    Article  ADS  Google Scholar 

  31. R. Voinea, N. Pandrea, Contribution to a general mathematical theory of kinematic linkages, in Proceedings of IFTOMM International Symposium on Linkages and Computer Design Method B (Bucharest, 1973), pp. 522–534

    Google Scholar 

  32. Y. Wang, T.M. Mason, Two-dimensional rigid-body collisions with friction. ASME J. Appl. Mech. 59(3), 635–642 (1992)

    Article  ADS  Google Scholar 

  33. W.L. Yao, C. Bin, C.S. Liu, Energetic coefficient of restitution for planar impact in multi-rigid-body systems with friction. Int. J. Impact Eng. 31(3), 255–265 (2005)

    Article  Google Scholar 

  34. L. Woo, F. Freudenstein, Application of line geometry to theoretical kinematics and the kinematic analysis of mechanical systems. J. Mech. 5(3), 417–460 (1970)

    Article  Google Scholar 

  35. H.N. Yu, J.S. Zhao, F.L. Chu, An enhanced multi-point dynamics methodology for collision and contact problems. Proc. Inst. Mech. Eng. Part C J. Mech. Eng. Sci. 227(6), 1203–1223 (2013)

    Article  Google Scholar 

  36. M. Yuan, F. Freudenstein, Kinematic analysis of spatial mechanisms by means of screw coordinates. ASME J. Eng. Ind. 93(1), 61–73 (1973)

    Article  Google Scholar 

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Author information

Authors and Affiliations

  1. University of Pitesti, Pitesti, 110040, Romania

    Ionuț-Bogdan Dragna, Nicolae Pandrea, Nicolae-Doru Stănescu & Dinel Popa

Authors
  1. Ionuț-Bogdan Dragna
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  2. Nicolae Pandrea
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  3. Nicolae-Doru Stănescu
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  4. Dinel Popa
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Corresponding author

Correspondence to Nicolae-Doru Stănescu .

Editor information

Editors and Affiliations

  1. Department of Mechanics and Strength of Materials, University Politehnica Timisoara, Timisoara, Romania

    Nicolae Herisanu

  2. Department of Mechanics and Strength of Materials, University Politehnica Timisoara, Timisoara, Romania

    Vasile Marinca

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Dragna, IB., Pandrea, N., Stănescu, ND., Popa, D. (2021). Vibrations with Collisions of a Mechanical System with Elastic Elements. In: Herisanu, N., Marinca, V. (eds) Acoustics and Vibration of Mechanical Structures—AVMS 2019. Springer Proceedings in Physics, vol 251. Springer, Cham. https://doi.org/10.1007/978-3-030-54136-1_7

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