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Flexibility Effects in Multibody Systems

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Computer-Aided Analysis of Rigid and Flexible Mechanical Systems

Part of the book series: NATO ASI Series ((NSSE,volume 268))

Abstract

This paper summarizes procedures for studying flexible multibody systems using finite segment modelling. In these procedures flexible members of multibody systems are themselves modelled as multibody (or “lumped”) systems. The flexibility is then modelled by springs and dampers between the bodies. Although the method has the disadvantage of being computationally intensive, the procedures presented are intended to ease the computational burden by efficient modelling and by efficient analytical formulations. It is believed that this approach combined with finite element and modal analysis methods can provide a comprehensive global and local analysis. Two examples are presented.

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References

  1. O.P. Agrawal and A.A. Shabana, “Dynamic analysis of multibody systems using component modes”, Comp. Struct.,21 1303–1312 (1985).

    Article  Google Scholar 

  2. M.L. Amirouche “Flexibility effects - estimation of the stiffness matrix in the dynamics of large structures”, J. Vib. Acoust. Stress Reliab. Des., 109 283–288 (1987).

    Article  Google Scholar 

  3. M.L. Amirouche “Dynamic analysis of tree-like structure undergoing large motions - A finite segment approach”, Eng. Analysis, 3, 111–117 (1986).

    Article  Google Scholar 

  4. F.M.L. Amirouche and R.L. Huston, “Dynamics of large constrained flexible structures”, J. Dyn. Syst. Meas. Control, 110, 78–83 (1988).

    Article  Google Scholar 

  5. H. Ashley “On passive damping mechanisms in large space structures”, J. Spacecraft Rockets, 21 448–455 (1984).

    Article  Google Scholar 

  6. P.M. Bainum, R. Krishna and V.K. Kuman, ‘The dynamics of large flexible earth painting structures with a hybrid control system“, J. Astronaut. Sci., xxx, 251–267 (1982).

    Google Scholar 

  7. E.M. Baker and A.A. Shabana, “Geometrically nonlinear analysis of multibody systems”, Comput. Struct., 23, 739–751 (1986).

    Article  Google Scholar 

  8. A.K. Banerjee and J.M. Dickens, “Dynamics of an arbitrary flexible body in large relations and translation”, J. Guid. Control Dyn., 13 221–227 (1990).

    Article  Google Scholar 

  9. A.K. Banerjee and M.E. Lemak, “Multi-flexible body dynamics capturing motion-induced stiffness”, J. AppL Mech.,58 766–775 (1991).

    Article  Google Scholar 

  10. H. Baruh and S.S.K. Tadikonda, “Issues in the dynamics and control of flexible robot manipulators”, J. Guid. Control Dyn., 12 659–671 (1989).

    Article  MathSciNet  MATH  Google Scholar 

  11. C.E. Benedict and D. Tesar, “Dynamic response analysis of quasi-rigid mechanical systems using kinematic influence coefficients”, J. Mechanisms, 6 383–403 (1971).

    Article  Google Scholar 

  12. P. Boland, J.C. Samin and P.Y. Willems, “Stability analysis of interconnected deformable bodies in a topological tree”, AIAA J., 12 1025–1030 (1974).

    Article  MathSciNet  MATH  Google Scholar 

  13. H. Bremer, “Dynamics of flexible hybrid structures,” J. Guidance and Control, 2, 86–87 (1979).

    Article  Google Scholar 

  14. R.H. Cannon, Jr. and E. Schmitz, “Initial experiments on the end-point control of a flexible one-link robot,” Int. J. Robotics Res., 3, 62–75 (1984).

    Article  Google Scholar 

  15. N.G. Chalhoub and A.G. Ulsoy, “Control of a flexible robot arm: Experimental and theoretical results”, ASME Paper 87-WA/DSC-3 (1987).

    Google Scholar 

  16. S. Dubowsky and T.N. Gardner, “Design and analysis of multilink flexible mechanisms with multiple clearance connections”, J. Eng. Industry ASME, 99 88–96 (1977).

    Article  Google Scholar 

  17. S. Dubowsky and M.F. Moening, “An experimental and analytical study of impact forces in elastic”, Mech. Mach. Theory, 13, 451–465 (1978).

    Article  Google Scholar 

  18. A.G. Erdman, G.N. Sandor and R.G. Oakberg, “A general method for kinetoelastodynamic analysis and synthesis of mechanisms,”J. Eng. Industry ASME, 94 1193–1205 (1972).

    Article  Google Scholar 

  19. W.B. Gevarter “Basic relations for control of flexible vehicles,” AIAA J., 8 666–678 (1970).

    Article  Google Scholar 

  20. R.P.S. Han and Z.C. Zhao, “Dynamics of general flexible multibody systems”, Int. J. Numer. Methods Eng., 30 77–97 (1990).

    Article  MATH  Google Scholar 

  21. J.Y.L. Ho “Direct path method for flexible multibody spacecraft dynamics”, J. Spacecraft Rockets, 14 102–110 (1977).

    Article  Google Scholar 

  22. J.Y.L. Ho and R. Gluck, “Inductive methods for generating the dynamic equations of motion for multibody flexible systems Part 2”, Synthesis of Vibrating Systems, ASME, New York, 1971.

    Google Scholar 

  23. J.Y.L. Ho and D.R. Herber, “Development of dynamics and control simulation of large flexible space systems”, J. Guid. Control Dyn., 8 374–383 (1985).

    Article  MATH  Google Scholar 

  24. Y. Huang and C.S.G. Lee, “Generalization of Newton-Euler formulation of dynamic equations to nonrigid manipulators”, J. Dyn. Syst. Meas. Control, 110 308–315 (1988).

    Article  MATH  Google Scholar 

  25. P.C. Hughes, “Dynamics of a chain of flexible bodies”, J. Astronaut. Sci., XXVII, 359–380 (1979).

    Google Scholar 

  26. P.C. Hughes, “Dynamics of a flexible space vehicle with active attitude control”, Celestial Mech. J., 9 21–39 (1974).

    Article  MATH  Google Scholar 

  27. R.L. Huston, “Flexibility effects in multibody systems”, Mech. Res. Commun., 7 261–268 (1980).

    Article  MATH  Google Scholar 

  28. R.L. Huston “Multibody dynamics including the effects of flexibility and compliance”, Comp. Struct.,14 443–451 (1981).

    Article  Google Scholar 

  29. R.L. Huston, “Multibody dynamics: Analysis of flexibility effects”, Proc. Ninth U.S. National Congress of Applied Mechanics, Cornell University, ASME, New York, 1982.

    Google Scholar 

  30. R.L. Huston, “Computer methods in flexible multibody dynamics”, Int. J. Numer. Methods Eng., 32, 1657–1668 (1991).

    Article  Google Scholar 

  31. I. Imam, G.N. Sandor and S.N. Kramer, “Deflection and stress analysis in high speed planar mechanisms with elastic links”, J. Eng. Industry ASME, 95 541–548 (1973).

    Article  Google Scholar 

  32. W. Jerkovsky “Exact equations of motion for a deformable body”, Aerospace Corporation, SA, SO-TR-77–133 (1977).

    Google Scholar 

  33. J.J. Kalker and G.J. Olsder, “Robots, with flexible links: Dynamics, control and stability”, NTIS Report PB86–174885 (1985).

    Google Scholar 

  34. T.R. Kane, P.R. Ryan and A.K. Banerjee, “Dynamics of a cantilever beam attached to a moving base”, J. Guid Control Dyn., 10 139–151 (1987).

    Article  Google Scholar 

  35. D.A. Levinson, “Large motions of unrestrained structures”, Proc. Ninth U.S. National Congress of Applied Mechanics, Cornell University, ASME, New York, 259–264 (1982).

    Google Scholar 

  36. P.W. Likins, “Dynamic analysis of a system of hinge-connected rigid bodies with nonrigid appendages”, Int. J. Solids Struct., 9 1473–1487 (1973).

    Article  MATH  Google Scholar 

  37. P.W. Likins, “Quasi-coordinate equations for flexible spacecraft”, AIAA J., 13 524–526 (1975).

    Article  MathSciNet  Google Scholar 

  38. P.W. Likins and H.K. Bouvier, “Attitude control of nonrigid spacecraft”,Astonaut. Aeronaut., 9 No. 5, 64–71 (1971).

    Google Scholar 

  39. K.W. Lipps and V.J. Modi, ‘Transient attitude dynamics of satellites with deploying flexible appendages“, Acta Astronaut., 5 797–815 (1978).

    Article  Google Scholar 

  40. KW. Lipps and V.J. Modi, “General dynamics of a large class of flexible satellite systems”, Acta Astronaut., 7 1349–1360 (1980).

    Article  Google Scholar 

  41. V.J. Modi “Attitude dynamics of satellites with flexible appendages - A brief review”, J. Spacecraft Rockets, 11 743–751 (1974).

    Article  Google Scholar 

  42. C.E. Padilla and A.H. Von Flotow, “Nonlinear-displacement relations and flexible multibody dynamics,” J. Guid. Control Dyn., 10 139–151 (1987).

    Article  Google Scholar 

  43. M. Pascal “Dynamical analysis of a flexible manipulator arm”, Acta Astronaut., 21 161–169 (1990).

    Article  MATH  Google Scholar 

  44. S. Rajaram and J.L. Junkins, “Identification of vibrating flexible structures”, J. Guid. Control. 8 463–370 (1985).

    Article  MATH  Google Scholar 

  45. J.P. Sadler and G.N. Sander, “A lumped parameter approach to vibration and stress analysis of elastic linkages”, J. Eng. Industry ASME, 95 549–557 (1973).

    Article  Google Scholar 

  46. A.A. Shabana “On the use of the finite element method and classical approximation techniques in the non-linear dynamics of multibody system”, Int. J. Non-linear Mech., 25 153–162 (1990).

    Article  MATH  Google Scholar 

  47. A.A. Shabana “Substructure synthesis methods for dynamic analysis of multi-body systems”, Comp. Struct., 20 737–744 (1985).

    Article  MATH  Google Scholar 

  48. R.C. Winfrey “Elastic link mechanisms dynamics”J. Eng. Industry ASME, 268–272 (1971).

    Google Scholar 

  49. T.R. Kane, “Dynamics of nonholonomic systems”, J. Appl. Mech. ASME, 28 574–578 (1961).

    Article  MathSciNet  MATH  Google Scholar 

  50. T.R. Kane, Dynamics, Holt, Rinehart and Winston,New York (1968).

    MATH  Google Scholar 

  51. T.R. Kane, P.W. Likins and D.A. Levinson, Spacecraft Dynamics, McGraw-Hill, New York (1983).

    Google Scholar 

  52. T.R. Kane and D.A. Levinson, Dynamics: Theory and Application, McGraw-Hill, New York (1985).

    Google Scholar 

  53. R.L. Huston and C.E. Passerello, “On multi-rigid body-systems dynamics”, Comp. Struct., 10 439–446 (1979).

    Article  MATH  Google Scholar 

  54. R.L. Huston, C.E. Passerello and M.W. Harlow, “Dynamics of multirigid body systems”, J. Appl. Mech. ASME, 45 889–894 (1978).

    Article  Google Scholar 

  55. R.L. Huston and C.E. Passerello, “Multibody structural dynamics including translation between the bodies”, Comp. Struct., 18 999–1003 (1984).

    Article  MATH  Google Scholar 

  56. R.L. Huston, “Multibody dynamics formulations via Kane’s equations”, in J.L. Junkins (ed.), Mechanics and Control of Large Space Structures, Vol. 129 of Progress in Astronautics and Aeronautics,AIAA, 71–86 (1990).

    Google Scholar 

  57. E.T. WhittakerAnalytical Dynamics, Cambridge (1957).

    Google Scholar 

  58. R.L. Huston, Multibody Dynamics, Butterworth-Heinmann, Stoneham, MA (1990).

    Google Scholar 

  59. R.L. Huston “Computing angular velocity in multibody systems”, Eng. Computations,3, 223–230 (1986).

    Article  Google Scholar 

  60. J.W. Kamman, R.L. Huston and T.P. King, “UCIN-DYNOCOMBS - Software for the dynamic analysis of constrained multibody systems”, in W. Schielen (ed.), Multibody Systems Handbook, Springer-Verlag, Berlin, 103–121 (1990).

    Google Scholar 

  61. T.R. Kane and C.F. Wang, “On the derivation of equations of motion”, J. Soc. Industrial Appl. Math., 13, 487–492 (1965).

    Article  MathSciNet  MATH  Google Scholar 

  62. T.R. Kane, Analytical Elements of Mechanics, 1, Academic Press, New York (1959).

    Google Scholar 

  63. R.L. Huston and C.E. Passerello, Finite Element Methods - An Introduction, marcel Dekker, New York (1985).

    Google Scholar 

  64. Y. Wang and R.L. Huston, “Dynamic analysis of elastic beam-like mechanism systems”, in A. Midha (ed.), Trends and Developments in Mechanisms, Machines and Robotics - 1988, DE-15–2, 457–460 (1988).

    Google Scholar 

  65. W. Weaver, Jr., S.P. Timoshenko and D.H. Young, Vibration Problems in Engineering, 5th edn, Wiley, New York, 427–428 (1990).

    Google Scholar 

  66. L.S. Jacobson and R.S. Ayre, Engineering Vibration, McGraw-Hill, 496 (1958).

    Google Scholar 

  67. W. Schiehlen (ed.), Multibody Systems Handbook, Springer-Verlag, Berlin (1990).

    MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Mechanical Industrial, and Nuclear Engineering, University of Cincinnati, Cincinnati, OH 45221-0072, USA

    R. L. Huston & Y. Wang

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  1. R. L. Huston
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  2. Y. Wang
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Editors and Affiliations

  1. Instituto de Engenharia Mecânica, Instituto Superior Técnico, Lisboa, Portugal

    Manuel F. O. Seabra Pereira  & Jorge A. C. Ambrósio  & 

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© 1994 Springer Science+Business Media Dordrecht

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Huston, R.L., Wang, Y. (1994). Flexibility Effects in Multibody Systems. In: Seabra Pereira, M.F.O., Ambrósio, J.A.C. (eds) Computer-Aided Analysis of Rigid and Flexible Mechanical Systems. NATO ASI Series, vol 268. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-1166-9_11

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  • DOI: https://doi.org/10.1007/978-94-011-1166-9_11

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-4508-7

  • Online ISBN: 978-94-011-1166-9

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