Nonlinear Dynamics

, Volume 4, Issue 6, pp 573–603

The dynamic stability and nonlinear resonance of a flexible connecting rod: Continuous parameter model

  • Shang-Rou Hsieh
  • Steven W. Shaw
Article

Abstract

The transverse vibrations of a flexible connecting rod in an otherwise rigid slider-crank mechanism are considered. An analytical approach using the method of multiple scales is adopted and particular emphasis is placed on nonlinear effects which arise from finite deformations. Several nonlinear resonances and instabilities are investigated, and the influences of important system parameters on these resonances are examined in detail.

Key words

Slider-crank mechanism nonlinear resonance dynamic stability method of multiple scales 

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References

  1. 1.
    Chu, S. and Pan, K. C., ‘Dynamic responses of a high-speed slider-crank mechanism with an elastic connecting rod,’ASME Journal of Engineering for Industry 97, 1975, 542–550.Google Scholar
  2. 2.
    Golebiewski, E. P. and Sadler, J. P., ‘Analytical and experimental investigation of elastic slider-crank mechanisms,’ASME Journal of Engineering for Industry 93, 1976, 1266–1271.Google Scholar
  3. 3.
    Sutherland, G. H., ‘Analytical and experimental investigation of a high-speed elastic-member linkage,’ASME Journal of Engineering for Industry 98, 1976, 788–794.Google Scholar
  4. 4.
    Viscomi, B. V. and Ayre, R. S., ‘Nonlinear dynamics response of elastic slider crank mechanism,’ASME Journal of Engineering for Industry,93, 1917, 251–262.Google Scholar
  5. 5.
    Erdman, A. G. and Sandor, G. N., ‘Kineto-elastodynamics-a review of the state of the art trends,’Mechanism and Machine Theory 7, 1972, 19–33.Google Scholar
  6. 6.
    Lowen, G. G. and Jandrasits, W. G., ‘Survey of investigation into the dynamic behavior of mechanisms containing links with distributed mass and elasticity,’Mechanism and Machine Theory 7, 1972, 3–17.Google Scholar
  7. 7.
    Lowen, G. G. and Chassapis, C., ‘The elastic behavior of linkages: An update,’Mechanism and Machine Theory 21, 1986, 33–42.Google Scholar
  8. 8.
    Thompson, B. S. and Sung, C. K., ‘A survey of finite element techniques for mechanism design,’Mechanism and Machine Theory,21, 1986, 351–359.Google Scholar
  9. 9.
    Neubauer, A. H.Jr., Cohen, R., and Hall, A. S.Jr., ‘An analytical study of the dynamics of an elastic linkage,’ASME Journal of Engineering for Industry,88, 1966, 311–317.Google Scholar
  10. 10.
    Jasinski, P. W., Lee, H. C., and Sandor, G. N., ‘Stability and steady-state vibrations in a high-speed slider-crank mechanism,’Journal of Applied Mechanics 37, 1970, 1069–1076.Google Scholar
  11. 11.
    Jasinski, P. W., Lee, H. C., and Sandor, G. N., ‘Vibration of elastic connecting rod of a high-speed slider-crank mechanism,’ASME Journal of Engineering for Industry 93, 1971, 636–644.Google Scholar
  12. 12.
    Badlani, M. and Kleinhenz, W., ‘Dynamic stability of elastic mechanisms,’ASME Journal of Mechanical Design 101, 1979, 149–153.Google Scholar
  13. 13.
    Tadjbakhsh, I. G., ‘Stability of motion of elastic planar linkage with application to slider-crank mechanism,’ASME Journal of Mechanical Design 104, 1982, 698–703.Google Scholar
  14. 14.
    Zhu, Z. G. and Chen, Y., ‘The stability of the motion of a connecting rod,’ASME Journal of Mechanism, Transmission, and Automation Design 105, 1983, 637–640.Google Scholar
  15. 15.
    Badlani, M. and Midha, A., ‘Effect of internal material damping on the dynamics of a slider-crank mechanism,’ASME Journal of Mechanisms, Transmission, and Automation Design 105, 1983, 452–459.Google Scholar
  16. 16.
    Farhang, K. and Midha, A., ‘Investigation of parametric vibration stability in slider-crank mechanism with elastic coupler’,Proceeding of 13th ASME Conference on Mechanical Vibration and Noise De-Vol. 37. Miami, FL, October 1991, 167–176.Google Scholar
  17. 17.
    Beale, D. and Lee. S.-W., ‘Investigation of parametric resonance stability in a flexible rod slider crank mechanism’,Proceeding of 13th ASME Conference on Mechanical Vibration and Noise De-Vol. 37. Miami, FL, October 1991, 161–166.Google Scholar
  18. 18.
    Beale, D. G. and Lee. S.-W., ‘Steady state response of a slider crank with flexible rod’,Nonlinear Dynamics (to appear).Google Scholar
  19. 19.
    Beal, D. and Halbig, D., ‘Experimental high speed response of a slider crank‘, inFourth Conference on Nonlinear Vibration, Stability, and Dynamics of Structures and Mechanisms, Blacksburg, VA, June 7–11, 1992.Google Scholar
  20. 20.
    Hsieh, S.-R. and Shaw, S. W., ‘Dynamic stability and nonlinear resonance of a flexible connecting rod: Single mode model’,Journal of Sound and Vibration (to appear).Google Scholar
  21. 21.
    Ryan, R. R. ‘Flexibility modeling methods in multibody dynamics, Ph.D. Thesis, Stanford University, 1986.Google Scholar
  22. 22.
    Yoo, Hong Hee, ‘Dynamic modeling of flexible bodies in multibody systems’, Ph.D. Thesis, University of Michigan, 1988.Google Scholar
  23. 23.
    Greenwood, D. T.,Principles of Dynamics, Prentice-Hall, Inc., Englewood Cliffs, NJ, 1969.Google Scholar
  24. 24.
    Housner, H.,Applied Mechanics Dynamics, Van Nostrand, Princeton, NJ, 1959.Google Scholar
  25. 25.
    Timoshenko, S.,Vibration Problem in Engineering, Van Nostrand, Princeton, NJ, 1990.Google Scholar
  26. 26.
    Nayfeh, A. H. and Mook, D. T.,Nonlinear Oscillations, Wiley Interscience, New York, NY, 1979.Google Scholar
  27. 27.
    Dym, C. L. and Shames, I. H.,Solid Mechanics, A Variational Approach, McGraw-Hill, New York, NY, 1973.Google Scholar
  28. 28.
    Hsieh, S.-R., ‘Nonlinear vibrations of a flexible connecting rod’, Ph.D. Thesis, Michigan State University, 1991.Google Scholar
  29. 29.
    Wiggins, S.,Introduction to Applied Nonlinear Dynamical Systems and Chaos, Springer-Verlag, New York, NY, 1990.Google Scholar
  30. 30.
    Guckenheimer, J. and Holmes, P.,Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields, Springer-Verlag, New York, NY, 1983.Google Scholar
  31. 31.
    Cronin, D. L. and Liu H., ‘Finite element analysis of the steady-state behavior of flexible mechanisms’, inThe First National Applied Mechanisms and Robotics Conference, Cincinnati, OH, November 1989.Google Scholar
  32. 32.
    Simo, J. C. and Vu-Quoc, L., ‘On the dynamic of flexible beam under large overall motions-the plane case: Part 1,’ASME Journal of Applied Mechanics 53, 1986, 849–854.Google Scholar
  33. 33.
    Simo, J. C. and Vu-Quoc, L., ‘On the dynamic of flexible beam under large overall motions-the plane case: Part II,’ASME Journal of Applied Mechanics 53, 1986, 855–863.Google Scholar

Copyright information

© Kluwer Academic Publishers 1993

Authors and Affiliations

  • Shang-Rou Hsieh
    • 1
  • Steven W. Shaw
    • 1
  1. 1.Department of Mechanical Engineering and Applied MechanicsThe University of MichiganAnn ArborU.S.A.

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