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All issues Volume 17 / No 4 (2016) Mechanics & Industry, 17 4 (2016) 409 References
Open Access
Issue
Mechanics & Industry
Volume 17, Number 4, 2016
Article Number 409
Number of page(s) 11
DOI https://doi.org/10.1051/meca/2015097
Published online 23 May 2016
  1. A.H. Nayfeh, Nonlinear oscillations, Wiley, New York, 1995 [Google Scholar]
  2. S.H. Strogatz, Nonlinear Dynamics and Chaos: with Applications to Physics, Biology, Chemistry, and Engineering, Addison-wesley, Reading, MA, 1994 [Google Scholar]
  3. F. Verhulst, Nonlinear Differential Equations and Dynamical Systems, 2nd edition, Springer, Berlin, 1999 [Google Scholar]
  4. R. Rand, Lecture Notes on Nonlinear Vibrations, Cornell, New York, USA, 2003 [Google Scholar]
  5. R.M. Rosenberg, On nonlinear vibrations of systems with many degrees of freedom, Adv. Appl. Mech. 9 (1966) 155–242 [Google Scholar]
  6. R.H. Rand, C.H. Pak, A.F. Vakakis, Bifurcation of nonlinear normal modes in a class of two degree of freedom systems, Acta Mechanica 3 (1992) 129–145 [Google Scholar]
  7. A.F. Vakakis, T. Nayfeh, M.E. King, A multiple scales analysis of nonlinear, localized modes in a cyclic periodic system, J. Appl. Mech. 60 (1993) 388–397 [CrossRef] [MathSciNet] [Google Scholar]
  8. M.E. King, A.F. Vakakis, Mode localization in a system of coupled flexible beams with geometric nonlinearities, Zeit. Angew. Math. Mech. (ZAMM) 75 (1995) 127–139 [CrossRef] [Google Scholar]
  9. A.F. Vakakis, L.I. Manevitch, Y.V. Mikhlin, V.N. Pilichuk, A.A. Zevin, Normal Modes and Localization in Nonlinear Systems, Wiley, New York, 1996 [Google Scholar]
  10. R. Rand, A direct method for nonlinear normal modes, Int. J. Non-Linear Mech. 9 (1974) 363–368 [CrossRef] [Google Scholar]
  11. S.W. Shaw, C. Pierre, Normal modes for non-linear vibratory systems, J. Sound Vib. 164 (1993) 85–124 [CrossRef] [Google Scholar]
  12. A.F. Vakakis, Non-linear normal modes and their applications in vibration theory: an overview, Mech. Syst. Signal Process. 11 (1997) 3–22 [CrossRef] [Google Scholar]
  13. A.H. Nayfeh, Introduction to Perturbation Techniques, Wiley-Interscience, New York, 1981 [Google Scholar]
  14. R.E. O’Malley, Singular Perturbation Methods for Ordinary Differential Equations, Springer, New York, 1991 [Google Scholar]
  15. J. Kevorkian, J.D. Cole, Multiple Scales and Singular Perturbation Methods, Springer, New York, 1996 [Google Scholar]
  16. H.S.Y. Chan, K.W. Chung, Z. Xu, A perturbation-incremental method for strongly non-linear oscillators, Int. J. Non-Linear Mech. 31 (1996) 59–72 [CrossRef] [Google Scholar]
  17. S.H. Chen, Y.K. Cheung, A modified Lindstedt-Poincare’ method for a strongly nonlinear two degree-of-freedom system, J. Sound Vib. 193 (1996) 751–762 [CrossRef] [Google Scholar]
  18. V.N. Pilipchuk, The calculation of strongly nonlinear systems close to vibration-impact systems, PMM 49 (1985) 572–578 [Google Scholar]
  19. L.I. Manevitch, Complex Representation of Dynamics of Coupled Oscillators in Mathematical Models of Nonlinear Excitations, Transfer Dynamics and Control in Condensed Systems, Kluwer Academic/Plenum Publishers, New York, 1999 [Google Scholar]
  20. M.I. Qaisi, A.W. Kilani, A power-series solution for a strongly non-linear two-degree-of-freedom system, J. Sound Vib. 233 (2000) 489–494 [CrossRef] [Google Scholar]
  21. V.I. Babitsky, V.L. Krupenin, Vibrations of Strongly Nonlinear Discontinuous Systems, Springer, Berlin, 2001 [Google Scholar]
  22. M.A. Rotea, F.J. D’Amato, Efficient algorithms for mistuning analysis, in: Proceedings of the 15th triennial world congress, Barcelona, Spain, 2003 [Google Scholar]
  23. M. Rahimi, S. Ziaei-Rad, Uncertainty treatment in forced response calculation of mistuned bladed disk, Math. Comput. Simul. 80 (2010) 1746–1757 [CrossRef] [Google Scholar]
  24. B.J. Olson, S.W. Shaw, Vibration absorbers for a rotating flexible structure with cyclic symmetry: nonlinear path design, Nonlinear Dynamics (2009) DOI: 10.1007/s11071-009-9587-8 [Google Scholar]
  25. H.H. Yoo, J.Y. Kim, D.J. Inman, Vibration localization of simplified mistuned cyclic structures undertaking external harmonic force, J. Sound Vib. 261 (2003) 859–870 [Google Scholar]
  26. M.E. King, Philip A. Layne, Dynamics of Nonlinear Cyclic Systems with Structural Irregularity, Nonlinear Dynamics 15 (1998) 225–244 [CrossRef] [MathSciNet] [Google Scholar]
  27. O. Gendelman, D. Gorlov, L. Manevitch, A. Musienko, Dynamics of coupled linear and essentially nonlinear oscillators with substantially different masses, J. Sound Vib. 286 (2005) 1–19 [CrossRef] [Google Scholar]
  28. Y.V. Mikhlin, S. Reshetnikova, Dynamical interaction of an elastic system and essentially nonlinear absorber, J. Sound Vib. 283 (2005) 91–120 [CrossRef] [Google Scholar]
  29. A.F. Vakakis, R.H. Rand, Non-linear dynamics of a system of coupled oscillators with essential stiffness non-linearities, Int. J. Non-Linear Mech. 39 (2004) 1079–1091 [CrossRef] [Google Scholar]
  30. A.F. Vakakis, L.I. Manevitch, O. Gendelman, L. Bergman, Dynamics of linear discrete systems connected to local, essentially non-linear attachments, J. Sound Vib. 264 (2003) 559–577 [CrossRef] [Google Scholar]
  31. D.M. McFarland, L.A. Bergman, A.F. Vakakis, Experimental study of non-linear energy pumping occurring at a single fast frequency, Int. J. Non-Linear Mech. 40 (2005) 891–899 [CrossRef] [Google Scholar]
  32. S. Pernot, E. Gourdon, C. Lamarque, M. Gloeckner, T. Griessmann, Experimental dynamics of a four-storey building coupled with a nonlinear energy sink, in: ENOC, Eindhoven, Netherlands, 2005 [Google Scholar]
  33. R.M. Rosenberg, The normal modes of nonlinear n-degrees-of-freedom systems, J. Appl. Mech. 30 (1962) 595–611 [Google Scholar]
  34. O.V. Gendelman, Bifurcations of nonlinear normal modes of linear oscillator with strongly nonlinear damped attachment, Nonlinear Dynamics 37 (2004) 115–128 [CrossRef] [MathSciNet] [Google Scholar]
  35. F.X. Wang, A.K. Bajaj, Nonlinear normal modes in multi-mode models of an inertially coupled elastic structure, Nonlinear Dynamics 47 (2007) 25–47 [CrossRef] [MathSciNet] [Google Scholar]
  36. W. Lacarbonara, G. Rega, A.H. Nayfeh, Resonant non-linear normal modes, Part I: analytical treatment for structural one-dimensional systems, Int. J. Non-Linear Mech. 38 (2003) 851–872 [CrossRef] [Google Scholar]
  37. W. Lacarbonara, G. Rega, Resonant non-linear normal modes, Part II: activation/orthogonality conditions for shallow structural systems, Int. J. Non-Linear Mech. 38 (2003) 873–887 [CrossRef] [Google Scholar]
  38. C.E.N. Mazzilli, O.G.P. Baracho Neto, Evaluation of non-linear normal modes for finite-element models, Comput. Struct. 80 (2002) 957–965 [CrossRef] [Google Scholar]
  39. X. Li, J.C. Ji, C.H. Hansen, Non-linear normal modes and their bifurcation of a two DOF system with quadratic and cubic non-linearity, Int. J. Non-linear Mech. 41 (2006) 1028–1038 [CrossRef] [Google Scholar]
  40. A. Grolet, F. Thouverez, Vibration analysis of a nonlinear system with cyclic symmetry, J. Eng. Gas Turbines Power 133 (2011) 022502 [CrossRef] [Google Scholar]
  41. F. Georgiades, M. Peeters, G. Kerschen, J. Golinval, Modal analysis of a nonlinear periodic structure with cyclic symmetry, AIAA J. 47 (2009) 1014–1025 [CrossRef] [Google Scholar]
  42. S. Samaranayake, G. Samaranayake, A.K. Bajaj, Resonant vibrations in harmonically excited weakly coupled mechanical systems with cyclic symmetry, Chaos, Solitons and Fractals 11 (2000) 1519–1534 [CrossRef] [MathSciNet] [Google Scholar]
  43. W. Sextro, K. Popp, T. Krzyzynski, Localization in Nonlinear Mistuned Systems with Cyclic Symmetry, Nonlinear Dynamics 25 (2001) 207–220 [CrossRef] [Google Scholar]
  44. J. Judge, C. Pierre, O. Mehmed, Experimental Investigation of Mode Localization and Forced Response Amplitude Magnification for a Mistuned Bladed Disk, J. Eng. Gas Turbines Power 123 (2001) 940–950 [Google Scholar]
  45. E.P. Petrov, D.J. Ewins, Analytical Formulation of Friction Interface Elements for Analysis of Nonlinear MultiHarmonics Vibrations of Bladed Disks, ASME J. Turbomachinery 125 (2003) 364371 [Google Scholar]
  46. E.P. Petrov, D.J. Ewins, Method for Analysis of Nonlinear Multiharmonic Vibrations of Mistuned Bladed Disks With Scatter of Contact Interface Characteristics. ASME J. Turbomachinery 127 (2006) 128136 [Google Scholar]
  47. E. Ciğeroğlu, H.N. Özgüven, Nonlinear vibration analysis of bladed disks with dry friction dampers, J. Sound Vib. 292 (2006) 10281043 [Google Scholar]
  48. Y.J. Yan, P.L. Cui, H.N. Hao, Vibration mechanism of a mistuned bladed-disk, J. Sound Vib. 317 (2008) 294–307 [CrossRef] [Google Scholar]
  49. B.K. Beachkofski, Probabilistic rotor life assessment using reduced order models, J. Shock Vib. 16 (2009) 581–591 [CrossRef] [Google Scholar]
  50. D. Laxalde, F. Thouverez, J.J. Sinou, J.P. Lombard, Qualitative analysis of forced response of blisks with friction ring dampers, Eur. J. Mech. A/Solids 26 (2007) 676–687 [CrossRef] [Google Scholar]
  51. S.H. Shin, M.K. Kang, H.H. Yoo, Mistuned coupling stiffness effect on the vibration localization of cyclic systems, J. Mech. Sci. Technol. 22 (2008) 269–275 [CrossRef] [Google Scholar]
  52. B. Salhi, J. Lardies, M. Berthillier, Identification of modal parameters and aeroelastic coefficients in bladed disk assemblies, Mech. Syst. Signal Process. 23 (2009) 1894–1908 [CrossRef] [Google Scholar]
  53. B. Zhou, F. Thouverez, D. Lenoir, An adaptive control strategy based on passive piezoelectric shunt techniques applied to mistuned bladed disks, J. Comput. Appl. Math. 246 (2013) 289–300 [CrossRef] [MathSciNet] [Google Scholar]
  54. B. Zhou, F. Thouverez, D. Lenoir, Essentially nonlinear piezoelectric shunt circuits applied to mistuned bladed disks, J. Sound Vib. 333 (2014) 2520–2542 [CrossRef] [Google Scholar]

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