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Review of Synchronization in Mechanical Systems

  • Mihir Sen
  • Carlos S. López CajúnEmail author
Chapter
Part of the Mechanisms and Machine Science book series (Mechan. Machine Science, volume 69)

Abstract

Synchronization of coupled sub-systems in both natural and engineered systems is a commonplace occurrence, but its existence and analysis in mechanical systems has received much less attention. This is a review, written for mechanical engineers, of some of the work done on complex machines that are in common use. Theoretical characteristics of the phenomena that are present are indicated by solutions to models based on self-excited oscillations. A variety of experiments on synchronization that have been carried out are reported, including work done by the authors on vibrations of rotor blades due to airflow and of automobile parts. A large number of references on the subject has been included so that a researcher who is new to synchronization in complex machinery can use this as a starting point.

Notes

Acknowledgements

This is to gratefully acknowledge the participation of Professor Juan Carlos Jáuregui Correa of the Universidad Autónoma de Querétaro who has been a co-author in some of the publications on which this review is based.

References

  1. 1.
    Mitchell, M.: Complexity: A Guided Tour. Oxford University Press, Oxford, U.K. (2009)zbMATHGoogle Scholar
  2. 2.
    Felippa, C.A., Park, K.C., Farhat, C.: Partitioned analysis of coupled mechanical systems. Comput. Methods Appl. Mech. Eng. 190(24–25), 3247–3270 (2001)zbMATHGoogle Scholar
  3. 3.
    Machado, J.A.T., Lopes, A.M.: Editorial: complex systems in mechanical engineering. Adv. Mech. Eng. 9(7), 1–3 (2017)Google Scholar
  4. 4.
    Strogatz, S.H.: Exploring complex networks. Nature 410(6825), 268–276 (2001)zbMATHGoogle Scholar
  5. 5.
    Wu, C.W.: Synchronization in Complex Networks of Nonlinear Dynamical Systems. World Scientific, Singapore (2007)zbMATHGoogle Scholar
  6. 6.
    Arenas, A., Díaz-Guilera, A., Kurths, J., Moreno, Y.: Synchronization in complex networks. Phys. Rep. 469(3), 93–153 (2008)MathSciNetGoogle Scholar
  7. 7.
    Latora, V., Nicosia, V., Russo, G.: Complex Networks: Principles, Methods and Applications. Cambridge University Press, Cambridge, U.K. (2017)zbMATHGoogle Scholar
  8. 8.
    Sen, M., Jáuregui-Correa, J.C., López, C.S.: Foreground and background components in separable complex systems. Systems 4(3) (2016)Google Scholar
  9. 9.
    Kutz, J.N., Fu, X., Brunton, S.L.: Multiresolution dynamic mode decomposition. SIAM J. Appl. Dyn. Syst. 15(2), 713–735 (2016)MathSciNetzbMATHGoogle Scholar
  10. 10.
    Gao, J., Cao, Y., Tung, W., Hu, J.: Multiscale Analysis of Complex Time Series: Integration of Chaos and Random Fractal Theory, and Beyond. Wiley, Hoboken, NJ (2007)zbMATHGoogle Scholar
  11. 11.
    Blekhman, I.I.: Synchronization in Science and Technology. ASME Press, New York (1988)Google Scholar
  12. 12.
    Rosenblum, M., Pikovsky, A.: Synchronization: from pendulum clocks to chaotic lasers and chemical oscillators. Contemp. Phys. 44(5), 401–416 (2003)Google Scholar
  13. 13.
    Pikovsky, A., Rosenblum, M., Kurths, J.: Synchronization: A Universal Concept in Nonlinear Sciences. Cambridge University Press (2003)Google Scholar
  14. 14.
    Nijmeijer, H., Rodriguez-Angeles, A.: Synchronization of Mechanical Systems. World Scientific, Singapore (2003)zbMATHGoogle Scholar
  15. 15.
    Pikovsky, A., Maistrenko, Y. (eds.): Synchronization: Theory and Application. Kluwer Academic Publishers, Dordrecht (2003)Google Scholar
  16. 16.
    Manrubia, S.C., Mikhailov, A.S., Zanette, D.H.: Emergence of Dynamical Order Synchronization Phenomena in Complex Systems. World Scientific, Singapore (2004)zbMATHGoogle Scholar
  17. 17.
    González-Miranda, J.M.: Synchronization and Control of Chaos: An Introduction for Scientists and Engineers. World Scientific, Singapore (2004)Google Scholar
  18. 18.
    Osipov, G.V., Kurths, J., Zhou, C.: Synchronization in Oscillatory Networks. Springer, Berlin (2007)zbMATHGoogle Scholar
  19. 19.
    Balanov, A., Janson, N., Postnov, D., Sosnovtseva, O.: Synchronization: From Simple to Complex. Springer, Berlin (2009)zbMATHGoogle Scholar
  20. 20.
    Boccaletti, S., Pisarchik, A.N., del Genio, C.I., Amann, A.: Synchronization: From Coupled Systems to Complex Networks. Cambridge University Press, Cambridge, U.K. (2018)zbMATHGoogle Scholar
  21. 21.
    Winfree, A.T.: The Geometry of Biological Time. Springer, New York (1980)zbMATHGoogle Scholar
  22. 22.
    Uchida, A.: Optical Communication with Chaotic Lasers: Applications of Nonlinear Dynamics and Synchronization. Wiley-UCH, Weinheim, Germany (2011)zbMATHGoogle Scholar
  23. 23.
    Strogatz, S.H., Stewart, I.: Coupled oscillators and biological synchronization. Sci. Am. 269(6), 102–109 (1993)Google Scholar
  24. 24.
    Strogatz, S.: Sync: How Order Emerges from Chaos in the Universe, Nature, and Daily Life. Hachette Books (2004)Google Scholar
  25. 25.
    Perlikowski, P., Stefanski, A., Kapitaniak, T.: Mode locking and generalized synchronization in mechanical oscillators. J. Sound Vib. 318, 329–340 (2008)Google Scholar
  26. 26.
    Koseska, A., Volkov, E., Kurths, J.: Oscillation quenching mechanisms: amplitude versus oscillation death. Phys. Rep. Rev. Sect. Phys. Lett. 531(4), 173–199 (2013)Google Scholar
  27. 27.
    Huygens, C.: The pendulum clock or geometrical demonstrations concerning the motion of pendula as applied to clocks. Blackwell, R.J. (trans., eds.) Edinburgh Books, Edinburgh, U.K. (1986)Google Scholar
  28. 28.
    C. Huygens. Letter to de Sluse, Letter No. 1333 of February 24, 1665, p. 241. Oeuvres Complète de Christiaan Huygens. Correspondence 5, 1664–1665; Société Hollandaise des Sciences, Martinus Nijhoff, 1893, La Haye, 2002Google Scholar
  29. 29.
    Yang, J., Wang, Y., Yu, Y.Z., Xiao, J.H., Wang, X.G.: Huygens’ synchronization experiment revisited: luck or skill? Eur. J. Phys. 39(5), Art. No. 055004 (2018)Google Scholar
  30. 30.
    Ganiev R.F., Fazullin, F.F.: On the non-linear synchronous oscillation and stability of turbine blades. Trudy Ufimsk aviats. in-ta 98 (1975)Google Scholar
  31. 31.
    Ganiev, R.F., Balakshin, O.B., Kukharenko, B.G.: On the occurrence of self-synchronization of auto-oscillations of turbo compressor rotor blades (original in Russian in Problemy Mashinostroeniya i Nadezhnosti Mashin, no. 6, pp. 16–23; J. Mach. Manuf. Reliab, 38(6), 535–541 (2009)Google Scholar
  32. 32.
    Ganiev, R.F., Balakshin, O.B., Kukharenko, B.G.: Flutter synchronization for turbo-compressor rotor blades (original in Russian in Doklady Akademii Nauk, vol. 427, no. 2, pp. 179–182); Dokl. Phys. 54(7), 312–315 (2009)Google Scholar
  33. 33.
    Quinn, D.D., Wang, F.: Synchronization of coupled oscillators through controlled energy transfer. Int. J. Bifurcat. Chaos 10(6), 1521–1535 (2000)MathSciNetzbMATHGoogle Scholar
  34. 34.
    Bennett, M., Schatz, M.F., Rockwood, H., Wiesenfeld, K.: Huygens’s clocks. Proc. Roy. Soc. A-Math. Phys. Eng. Sci. 458(2019), 563–579 (2002)MathSciNetzbMATHGoogle Scholar
  35. 35.
    Balthazar, J.M., Felix, J.L.P., Brasil, R.M.: Some comments on the numerical simulation of self-synchronization of four non-ideal exciters. Appl. Math. Comput. 164(2), 615–625 (2005)MathSciNetzbMATHGoogle Scholar
  36. 36.
    Peña Ramirez, J., Fey, R.H.B., Aihara, K., Nijmeijer, H.: An improved model for the classical Huygens’ experiment on synchronization of pendulum clocks. J. Sound Vib. 333(26), 7248–7266 (2014)Google Scholar
  37. 37.
    Jaros, P., Borkowski, L., Witkowski, B., Czolczynski, K., Kapitaniak, T.: Multi-headed chimera states in coupled pendula. Eur. Phys. J. Spec. Top. 224(8), 1605–1617 (2015)Google Scholar
  38. 38.
    Oliveira, H.M., Melo, L.V.: Huygens synchronization of two clocks. Sci. Rep. 5 (2015)Google Scholar
  39. 39.
    Dudkowski, D., Grabski, J., Wojewoda, J., Perlikowski, P., Maistrenko, Y., Kapitaniak, T.: Experimental multi-stable states for small network of coupled pendula. Sci. Rep. 6 (2016)Google Scholar
  40. 40.
    Peña Ramirez, J., Olvera, L.A., Nijmeijer, H., Alvarez, J.: The sympathy of two pendulum clocks: beyond Huygens’ observations. Sci. Rep. 6 (2016)Google Scholar
  41. 41.
    Bertram, C.D., Sheppeard, M.D.: Interactions of pulsatile upstream forcing with flow-induced oscillations of a collapsed tube: mode-locking. Med. Eng. Phys. 22(1), 29–37 (2000)Google Scholar
  42. 42.
    Glass, L.: Synchronization and rhythmic processes in physiology. Nature 410(6825), 277–284 (2001)Google Scholar
  43. 43.
    Hoppensteadt, F.C., Izhikevich, E.M.: Synchronization of MEMS resonators and mechanical neurocomputing. IEEE Trans. Circ. Syst. I-Regul. Pap. 48(2), 133–138 (2001)MathSciNetzbMATHGoogle Scholar
  44. 44.
    Woafo, P.: Transitions to chaos and synchronization in a nonlinear emitter-receiver system. Phys. Lett. A 267(1), 31–39 (2000)MathSciNetGoogle Scholar
  45. 45.
    Wu, S., Smith, S.L., Fork, R.L.: Kerr-lens-mediated dynamics of 2 nonlinearly coupled mode-locked laser-oscillators. Opt. Lett. 17(4), 276–278 (1992)Google Scholar
  46. 46.
    Roychowdhury, J.: Boolean computation using self-sustaining nonlinear oscillators. Proc. IEEE 103(11, SI), 1958–1969 (2015)Google Scholar
  47. 47.
    Ling, F.: Synchronization in Digital Communication Systems. Cambridge University Press, Cambridge, U.K. (2017)zbMATHGoogle Scholar
  48. 48.
    Rodrigues, F.A., Peron, T.K.D.M., Ji, P., Kurths, J.: The Kuramoto model in complex networks. Phys. Rep. Rev. Sect. Phys. Lett. 610, 1–98 (2016)MathSciNetzbMATHGoogle Scholar
  49. 49.
    Pecora, L.M., Carroll, T.l.: Synchronization of chaotic systems. Chaos 25(9) (2015)Google Scholar
  50. 50.
    Woafo, P., Fotsin, H.B., Chedjou, J.C.: Dynamics of two nonlinearly coupled oscillators. Phys. Scr. 57(2), 195–200 (1998)Google Scholar
  51. 51.
    Thwaites, F.W., Sen, M.: Dynamics of temperatures in thermally-coupled, heated rooms with PI control. In: Proceedings of the ASME IMECE 2007 Pts. A and B, Heat Transfer, Fluid Flows, and Thermal Systems, vol. 8, pp. 585–589 (2008)Google Scholar
  52. 52.
    Cai, W., Sen, M.: Synchronization of thermostatically controlled first-order systems. Int. J. Heat Mass Trans. 51(11–12), 3032–3043 (2008)zbMATHGoogle Scholar
  53. 53.
    O’Brien, J., Sen, M.: Temperature synchronization, phase dynamics and oscillation death in a ring of thermally-coupled rooms. In: Proceedings of the ASME IMECE 2011, Pts A and B, pp. 73–82 (2012)Google Scholar
  54. 54.
    Sen, M.: Effect of walls on synchronization of thermostatic room-temperature oscillations. Ingeniería Mecánica, Tecnología y Desarrollo 4(3), 81–88 (2012)Google Scholar
  55. 55.
    Sen, M., Amegashie, I., Cecconi, E., Antsaklis, P.: Dynamics of air and wall temperatures in multiroom buildings. In: Proceedings of the ASME IMECE 2012, vol. 10, pp. 263–272 (2013)Google Scholar
  56. 56.
    Cai, W., Sen, M., Yang, K.T., McClain, R.L.: Synchronization of self-sustained thermostatic oscillations in a thermal-hydraulic network. Int. J. Mass Transf. 49(23–24), 4444–4453 (2006)zbMATHGoogle Scholar
  57. 57.
    Barron, M.A., Sen, M.: Synchronization of temperature oscillations in heated plates with hysteretic on-off control. Appl. Therm. Eng. 65(1–2), 337–342 (2014)Google Scholar
  58. 58.
    Kitahata, H., Taguchi, J., Nagayama, M., Sakurai, T., Ikura, Y., Osa, A., Sumino, Y., Tanaka, M., Yokoyama, E., Miike, H.: Oscillation and synchronization in the combustion of candles. J. Phys. Chem. A 113(29), 8164–8168 (2009)Google Scholar
  59. 59.
    Crandall, S.H.: Foreward in [11]Google Scholar
  60. 60.
    Kuznetsov, Y.I., Minakova, I.I., Tshedrina, M.I.: Mutual synchronization mechanisms of 2 resonance coupled oscillators. Vestnik Moskovskogo Universiteta Seriya 3 Fizika Astronomiya, 31(3), 94–96 (1990)Google Scholar
  61. 61.
    Dimentberg, M., Cobb, E., Mensching, J.: Self-synchronization of transient rotations in multiple-shaft systems. J. Vib. Control 7(2), 221–232 (2001)zbMATHGoogle Scholar
  62. 62.
    Kuramoto, Y.: Chemical Oscillations, Waves, and Turbulence. Springer, New York (1984)zbMATHGoogle Scholar
  63. 63.
    Strogatz, S.H.: From Kuramoto to Crawford: exploring the onset of synchronization in populations of coupled oscillators. Phys. D 143(1–4), 1–20 (2000)MathSciNetzbMATHGoogle Scholar
  64. 64.
    Moreno, Y., Pacheco, A.F.: Synchronization of Kuramoto oscillators in scale-free networks. Europhys. Lett. 68(4), 603–609 (2004)Google Scholar
  65. 65.
    Dolmatova, A.V., Goldobin, D.S., Pikovsky, A.: Synchronization of coupled active rotators by common noise. Phys. Rev. E, 96(6) (2017)Google Scholar
  66. 66.
    Boccara, N.: Modeling Complex Systems. Springer, New York (2004)zbMATHGoogle Scholar
  67. 67.
    Pacheco-Vega, A., Diaz, G., Sen, M., Yang, K.T.: Applications of artificial neural networks and genetic methods in thermal engineering. In: Chhabra, R. (ed.) The CRC Handbook of Thermal Engineering, pp. 1217–1269, Section 4.27. CRC Press, Boca Raton, FL (2017)Google Scholar
  68. 68.
    Barron, M.A., Sen, M.: Dynamic behavior of a large ring of coupled self-excited oscillators. J. Comput. Nonlinear Dyn. 8(3) (2013)Google Scholar
  69. 69.
    Barron, M.A., Sen, M., Corona, E.: Dynamics of large rings of coupled Van der Pol oscillators. In: Elleithy, K. (ed.) Innovations and Advanced Techniques in Systems, Computing Sciences and Software Engineering, pp. 346–349 (2008); International Conference on Systems, Computing Science and Software Engineering, Electr Network, 03–12 Dec 2007Google Scholar
  70. 70.
    Barron, M.A., Sen, M.: Synchronization of four coupled van der Pol oscillators. Nonlinear Dyn. 56(4), 357–367 (2009)MathSciNetzbMATHGoogle Scholar
  71. 71.
    Kuznetsov, A.P., Roman, J.P.: Properties of synchronization in the systems of non-identical coupled van der Pol and van der Pol-Duffing oscillators. Broadband synchronization. Phys. D-Nonlinear Phenom. 38(6), 499–1506 (2009)MathSciNetzbMATHGoogle Scholar
  72. 72.
    Kibirkstis, E., Pauliukaitis, D., Miliunas, V., Ragulskis, K.: Synchronization of pneumatic vibroexciters under air cushion operating mode in a self-exciting autovibration regime. J. Mech. Sci. Technol. 31(9), 4137–4144 (2017)Google Scholar
  73. 73.
    Sun, Z., Xiao, R., Yang, X., Xu, W.: Quenching oscillating behaviors in fractional coupled Stuart-Landau oscillators. Chaos 28(3) (2018)Google Scholar
  74. 74.
    Vinod, V., Balaram, B., Narayanan, M.D., Sen, M.: Effect of oscillator and initial condition differences in the dynamics of a ring of dissipative coupled van der Pol oscillators. J. Mech. Sci. Technol. 29(5), 1931–1939 (2015)Google Scholar
  75. 75.
    Zhang, X., Wen, B., Zhao, C.: Theoretical study on synchronization of two exciters in a nonlinear vibrating system with multiple resonant types. Nonlinear Dyn. 85(1), 141–154 (2016)MathSciNetGoogle Scholar
  76. 76.
    Jiang, H., Liu, Y., Zhang, L., Yu, J.: Anti-phase synchronization and symmetry-breaking bifurcation of impulsively coupled oscillators. Commun. Nonlinear Sci. Numer. Simul. 39, 199–208 (2016)MathSciNetGoogle Scholar
  77. 77.
    Hou, Y., Fang, P., Nan, Y., Du, M.: Synchronization investigation of vibration system of two co-rotating rotors with energy balance method. Adv. Mech. Eng. 8(1) (2016)Google Scholar
  78. 78.
    Fang, P., Hou, Y.: Synchronization characteristics of a rotor-pendula system in multiple coupling resonant systems. Proc. Inst. Mech. Eng. Part C-J. Mech. Eng. Sci. 232(10), 1802–1822 (2018)Google Scholar
  79. 79.
    Vinod, V., Balaram, B., Narayanan, M.D., Sen, M.: Effect of configuration symmetry on synchronization in a Van der Pol ring with nonlocal interactions. Nonlinear Dyn. 89(3), 2103–2114 (2017)Google Scholar
  80. 80.
    Pantaleone, J.: Synchronization of metronomes. J. Phys. 70, 992 (2002)Google Scholar
  81. 81.
    Oud, W.T.: Design and experimental results of synchronizing metronomes, inspired by Christiaan Huygens. Master’s thesis, Eindhoven University of Technology, Eindhoven, Department of Mechanical Engineering (2006)Google Scholar
  82. 82.
    Kuznetsov, N.V., Leonov, G.A., Nijmeijer, H., Pogromsky, A.: Synchronization of two metronomes. IFAC Proc. 40(14), 49–52 (2007)Google Scholar
  83. 83.
    Martens, E.A., Thutupalli, S., Fourriere, A., Hallatschek, O.: Chimera states in mechanical oscillator networks. Proc. Natl. Acad. Sci. USA 110(26), 10563–10567 (2013)Google Scholar
  84. 84.
    Hoskoti, L., Misra, A., Sucheendran, M.M.: Frequency lock-in during vortex induced vibration of a rotating blade. J. Fluids Struct. 80, 145–164 (2018)Google Scholar
  85. 85.
    Barron, M.A., Sen, M.: Synchronization of coupled self-excited elastic beams. J. Sound Vib. 324(1–2), 209–220 (2009)Google Scholar
  86. 86.
    Wang, D., Zhao, C., Yao, H., Wen, B.: Vibration synchronization of a vibrating system driven by two motors. Adv. Vib. Eng. 11(1), 59–73 (2012)Google Scholar
  87. 87.
    Zhang, X.-L., Wen, B.-C., Zhao, C.-Y.: Synchronization of three homodromy coupled exciters in a non-resonant vibrating system of plane motion. Acta Mech. Sin. 28(5), 1424–1435 (2012)MathSciNetzbMATHGoogle Scholar
  88. 88.
    Wang, D., Chen, Y., Hao, Z., Cao, Q.: Bifurcation analysis for vibrations of a turbine blade excited by air flows. Sci. China-Technol. Sci. 59(8), 1217–1231 (2016)Google Scholar
  89. 89.
    Wang, D., Chen, Y., Wiercigroch, M., Cao, Q.: Bifurcation and dynamic response analysis of rotating blade excited by upstream vortices. Appl. Math. Mech.-Eng. Ed. 37(9), 1251–1274 (2016)MathSciNetzbMATHGoogle Scholar
  90. 90.
    Wang, D., Chen, Y., Wiercigroch, M., Cao, Q.: A three-degree-of-freedom model for vortex-induced vibrations of turbine blades. Meccanica 51(11, SI), 2607–2628 (2016)Google Scholar
  91. 91.
    Wang, D., Hao, Z., Chen, Y., Zhang, Y.: Dynamic and resonance response analysis for a turbine blade with varying rotating speed. J. Theor. Appl. Mach. 56(1), 31–42 (2018)Google Scholar
  92. 92.
    Oppenheim, A.V., Willsky, A.S., Hamid, S.: Signals and Systems. Pearson, 2nd edn. (1996)Google Scholar
  93. 93.
    Haykin, S., Van Veen, B. Signals and Systems. Wiley (2002)Google Scholar
  94. 94.
    Porat, B.: Digital Processing of Random Signals: Theory and Methods. Dover (2008)Google Scholar
  95. 95.
    Jáuregui, J.C., Sen, M., López-Cajún, C.S.: Experimental characterization of synchronous vibration of blades. In: Proceedings of the ASME Turbo Expo 2011, Pts A and B, vol. 6, pp. 821–828 (2012)Google Scholar

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Authors and Affiliations

  1. 1.Department of Aerospace and Mechanical EngineeringUniversity of Notre DameNotre DameUSA
  2. 2.División de Investigación y Posgrado, Facultad de Ingeniería, Departamento de Ingeniería MecánicaUniversidad Autónoma de QuerétaroQuerétaroMexico

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