Table of Contents Author Guidelines Submit a Manuscript
Shock and Vibration
Volume 2016, Article ID 3253178, 19 pages
http://dx.doi.org/10.1155/2016/3253178
Research Article

Analysis of Free Pendulum Vibration Absorber Using Flexible Multi-Body Dynamics

Mechanical Engineering Department, Texas Tech University, Lubbock, TX 79409, USA

Received 9 February 2016; Revised 3 July 2016; Accepted 11 July 2016

Academic Editor: Londono Monsalve

Copyright © 2016 Emrah Gumus and Atila Ertas. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. F. Salam and S. Sastry, “Dynamics of the forced Josephson junction: the regions of chaos,” IEEE Transanctions on Circuits and Systems, vol. 32, no. 8, pp. 784–796, 1985. View at Publisher · View at Google Scholar
  2. W. Lee, A global analysis of a forced spring pendulum system [Ph.D. thesis], University of California, Berkeley, Calif, USA, 1988.
  3. A. H. Nayfeh, D. T. Mook, and L. R. Marshall, “Nonlinear coupling of pitch and roll modes in ship motions,” Jornal of Hydrodynamics, vol. 7, no. 4, pp. 145–152, 1973. View at Publisher · View at Google Scholar · View at Scopus
  4. G. Mustafa, Three-dimensional rocking and topping of block-like structures on rigid foundation [M.S. thesis], Texas Tech University, Lubbock, Tex, USA, 1987.
  5. R. A. Ibrahim, Parametric Random Vibration, John Wiley & Sons, New York, NY, USA, 1985.
  6. A. H. Nayfeh and B. Balachandran, “Modal interactions in dynamical and structural systems,” Applied Mechanics Reviews, vol. 42, supplement 11, pp. S175–S201, 1989. View at Publisher · View at Google Scholar · View at MathSciNet
  7. A. H. Nayfeh, Nonlinear Interactions, Wiley, New York, NY, USA, 2000. View at MathSciNet
  8. E. Sevin, “On the parametric excitation of pendulum-type vibration absorber,” Journal of Applied Mechanics, vol. 28, no. 3, pp. 330–334, 1961. View at Publisher · View at Google Scholar
  9. J.-C. Nissen, K. Popp, and B. Schmalhorst, “Optimization of a non-linear dynamic vibration absorber,” Journal of Sound and Vibration, vol. 99, no. 1, pp. 149–154, 1985. View at Publisher · View at Google Scholar · View at Scopus
  10. A. Ertas and G. Mustafa, “Real-time response of the simple pendulum: an experimental technique,” Experimental Techniques, vol. 16, no. 4, pp. 33–35, 1992. View at Publisher · View at Google Scholar
  11. G. Mustafa and A. Ertas, “Dynamics and bifurcations of a coupled column-pendulum oscillator,” Journal of Sound and Vibration, vol. 182, no. 3, pp. 393–413, 1995. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  12. G. Mustafa and A. Ertas, “Experimental evidence of quasiperiodicity and its breakdown in the column-pendulum oscillator,” Journal of Dynamic Systems, Measurement and Control, vol. 117, no. 2, pp. 218–225, 1995. View at Publisher · View at Google Scholar · View at Scopus
  13. O. Cuvalci and A. Ertas, “Pendulum as vibration absorber for flexible structures: experiments and theory,” ASME Journal of Vibration and Acoustics, vol. 118, no. 4, pp. 558–566, 1996. View at Publisher · View at Google Scholar · View at Scopus
  14. W. Lacarbonara, R. R. Soper, A. H. Nayfeh, and D. T. Mook, “Nonclassical vibration absorber for pendulation reduction,” Journal of Vibration and Control, vol. 7, no. 3, pp. 365–393, 2001. View at Publisher · View at Google Scholar · View at Scopus
  15. I. Cicek and A. Ertas, “Experimental investigation of beam-tip mass and pendulum system under random excitation,” Mechanical Systems and Signal Processing, vol. 16, no. 6, pp. 1059–1072, 2002. View at Publisher · View at Google Scholar · View at Scopus
  16. K. E. Rifai, G. Haller, and A. K. Bajaj, “Global dynamics of an autoparametric spring-mass-pendulum system,” Nonlinear Dynamics, vol. 49, no. 1-2, pp. 105–116, 2007. View at Publisher · View at Google Scholar · View at Scopus
  17. B. Vazquez-Gonzalez and G. Silva-Navarro, “Evaluation of the autoparametric pendulum vibration absorber for a Duffing system,” Shock and Vibration, vol. 15, no. 3-4, pp. 355–368, 2008. View at Publisher · View at Google Scholar · View at Scopus
  18. N. Jiří and F. Cyril, “Auto-parametric semi-trivial and post-critical response of a spherical pendulum damper,” Computers & Structures, vol. 87, no. 19-20, pp. 1204–1215, 2009. View at Publisher · View at Google Scholar
  19. R. Viguié and G. Kerschen, “Nonlinear vibration absorber coupled to a nonlinear primary system: a tuning methodology,” Journal of Sound and Vibration, vol. 326, no. 3–5, pp. 780–793, 2009. View at Publisher · View at Google Scholar · View at Scopus
  20. A. Vyas and A. K. Bajaj, “Dynamics of autoparametric vibration absorbers using multiple pendulums,” Journal of Sound and Vibration, vol. 246, no. 1, pp. 115–135, 2001. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  21. R. S. Haxton and A. D. S. Barr, “The autoparametric vibration absorber,” Journal of Engineering for Industry, vol. 94, no. 1, pp. 119–225, 1972. View at Publisher · View at Google Scholar
  22. H. Hatwal, A. K. Mallik, and A. Ghosh, “Forced nonlinear oscillations of an autoparametric system—part 1: periodic responses,” Journal of Applied Mechanics, vol. 50, no. 3, pp. 657–662, 1983. View at Publisher · View at Google Scholar
  23. S. S. Oueini, A. H. Nayfeh, and J. R. Pratt, “A nonlinear vibration absorber for flexible structures,” Nonlinear Dynamics, vol. 15, no. 3, pp. 259–282, 1998. View at Publisher · View at Google Scholar · View at Scopus
  24. O. N. Ashour and A. H. Nayfeh, “Adaptive control of flexible structures using a nonlinear vibration absorber,” Nonlinear Dynamics, vol. 28, no. 3-4, pp. 309–322, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  25. S. S. Oueini and A. H. Nayfeh, “Analysis and application of a nonlinear vibration absorber,” Journal of Vibration and Control, vol. 6, no. 7, pp. 999–1016, 2000. View at Publisher · View at Google Scholar · View at Scopus
  26. E. Matta, A. De Stefano, and B. F. Spencer Jr., “A new passive rolling-pendulum vibration absorber using a non-axial-symmetrical guide to achieve bidirectional tuning,” Earthquake Engineering & Structural Dynamics, vol. 38, no. 15, pp. 1729–1750, 2009. View at Publisher · View at Google Scholar · View at Scopus
  27. W. Schiehlen, “Multibody system dynamics: roots and perspectives,” Multibody System Dynamics, vol. 1, no. 2, pp. 149–188, 1997. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  28. W. W. Hooker and G. Margulies, “The dynamical attitude equations for n-body satelite,” Journal of the Astronautical Sciences, vol. 12, pp. 123–128, 1965. View at Google Scholar · View at MathSciNet
  29. R. E. Roberson and J. Wittenburg, “A dynamical formalism for an arbitrary number of interconnected rigid bodies with reference to the problem of satellite attitude control,” in Proceedings of the 3rd Congress International Federation of Automatic Control, Warsaw, Poland, 1967.
  30. J. Wittenburg, Dynamics of Systems of Rigid Bodies, Teubner, Stuttgart, Germany, 1977.
  31. P. E. Nikravesh, Computer Aided Analysis of Mechanical Systems, Prentice-Hall, Upper Saddle River, NJ, USA, 1988.
  32. E. J. Haug, Computer Aided Kinematics and Dynamics of Mechanical Systems, Allyn and Bacon, Boston, Mass, USA, 1989.
  33. R. E. Roberson and R. Schwertassek, Dynamics of Multibody Systems, Springer, Berlin, Germany, 1988. View at Publisher · View at Google Scholar · View at MathSciNet
  34. R. L. Huston, Multibody Dynamics, Butterworth-Heinemann, Boston, Mass, USA, 1990.
  35. J. García de Jalón and E. Bayo, Kinematic and Dynamic Simulation of Multibody Systems, Mechanical Engineering Series, Springer, Berlin, Germany, 1994. View at Publisher · View at Google Scholar · View at MathSciNet
  36. O. P. Agrawal and A. A. Shabana, “Dynamic analysis of multibody systems using component modes,” Computers & Structures, vol. 21, no. 6, pp. 1303–1312, 1985. View at Publisher · View at Google Scholar · View at Scopus
  37. W. S. Yoo and E. J. Haug, “Dynamics of articulated structures: part I. Theory,” Journal of Structural Mechanics, vol. 14, no. 1, pp. 105–126, 1986. View at Publisher · View at Google Scholar · View at Scopus
  38. J. O. Song and E. J. Haug, “Dynamic analysis of planar flexible mechanisms,” Computer Methods in Applied Mechanics and Engineering, vol. 24, no. 3, pp. 359–381, 1980. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  39. A. A. Shabana, “Finite element incremental approach and exact rigid body inertia,” ASME Journal of Mechanical Design, vol. 118, no. 2, pp. 171–178, 1996. View at Publisher · View at Google Scholar · View at Scopus
  40. A. A. Shabana, Dynamics of Multibody Systems, Cambridge University Press, New York, NY, USA, 2005.
  41. C. C. Rankin and F. A. Brogan, “An element independent corotational procedure for the treatment of large rotations,” Journal of Pressure Vessel Technology, vol. 108, no. 2, pp. 165–174, 1986. View at Publisher · View at Google Scholar · View at Scopus
  42. J. C. Simo and L. Vu-Quoc, “On the dynamics of flexible beams under large overal motions—the plane case: part I,” Journal of Applied Mechanics, vol. 53, no. 4, pp. 849–854, 1986. View at Publisher · View at Google Scholar
  43. J. L. Escalona, H. A. Hussien, and A. A. Shabana, “Application of the absolute nodal coordinate formulation to multibody system dynamics,” Tech. Rep., University of Illinois at Chicago, Chicago, Ill, USA, 1997. View at Google Scholar
  44. J. L. Escalona, H. A. Hussien, and A. A. Shabana, “Application of the absolute nodal co-ordinate formulation to multibody system dynamics,” Journal of Sound and Vibration, vol. 214, no. 5, pp. 833–851, 1998. View at Publisher · View at Google Scholar · View at Scopus
  45. J. T. Sopanen and A. M. Mikkola, “Description of elastic forces in absolute nodal coordinate formulation,” Nonlinear Dynamics, vol. 34, no. 1-2, pp. 53–74, 2003. View at Publisher · View at Google Scholar · View at Scopus
  46. R. Iwai and N. Kobayashi, “A new flexible multibody beam element based on the absolute nodal coordinate formulation using the global shape function and the analytical mode shape function,” Nonlinear Dynamics, vol. 34, no. 1-2, pp. 207–232, 2003. View at Publisher · View at Google Scholar · View at Scopus
  47. O. Wallrapp and S. Wiedemann, “Comparison of results in flexible multibody dynamics using various approaches,” Nonlinear Dynamics, vol. 34, no. 1-2, pp. 189–206, 2003. View at Publisher · View at Google Scholar · View at MathSciNet
  48. A. A. Shabana, “Computer implementation of the absolute nodal coordinate formulation for flexible multibody dynamics,” Nonlinear Dynamics, vol. 16, no. 3, pp. 293–306, 1998. View at Publisher · View at Google Scholar · View at MathSciNet
  49. W.-S. Yoo, J.-H. Lee, S.-J. Park, J.-H. Sohn, O. Dmitrochenko, and D. Pogorelov, “Large oscillations of a thin cantilever beam: physical experiments and simulation using the absolute nodal coordinate formulation,” Nonlinear Dynamics, vol. 34, no. 1-2, pp. 3–29, 2003. View at Publisher · View at Google Scholar · View at Scopus
  50. W.-S. Yoo, J.-H. Lee, S.-J. Park, J.-H. Sohn, D. Pogorelov, and O. Dmitrochenko, “Large deflection analysis of a thin plate: computer simulations and experiments,” Multibody System Dynamics, vol. 11, no. 2, pp. 185–208, 2004. View at Publisher · View at Google Scholar · View at Scopus
  51. M. Berzeri and A. A. Shabana, “Development of simple models for the elastic forces in the absolute nodal co-ordinate formulation,” Journal of Sound and Vibration, vol. 235, no. 4, pp. 539–565, 2000. View at Publisher · View at Google Scholar · View at Scopus
  52. R. A. Wehage and E. J. Haug, “Generalized coordinate partitioning for dimension reduction in analysis of constrained dynamic systems,” Journal of Mechanical Design, vol. 104, no. 1, pp. 247–255, 1982. View at Google Scholar
  53. N. M. Newmark, “A method of computation for structural dynamics,” Journal of the Engineering Mechanics Division, vol. 85, no. 3, pp. 67–94, 1959. View at Google Scholar
  54. F. N. Mayoof, “Beating phenomenon of multi-harmonics defect frequencies in a rolling element bearing: case study from water pumping station,” World Academy of Science, Engineering and Technology, vol. 57, pp. 327–331, 2009. View at Google Scholar · View at Scopus