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DYnamique NOn LINéaire
[1] R.M. Rosenberg, Normal modes of
nonlinear dual-mode systems, Journal of Applied Mechanics, 27, (1960)
263-368.
[2] L. Jézéquel, C.H. Lamarque. Analysis of non linear dynamical systems by the normal form theory. Journal of Sound and Vibrations, 149(3), 429-459, 1991.
[3] S.W. Shaw, C. Pierre, Non linear normal modes for non linear vibratory systems, Journal of Sound and Vibrations, 164(1), 85-124, 1993.
[4] A.F. Vakakis, L.I. Manevitch, Yu.V. Mikhlin, V.N. Pilipchuk, A.A. Zevin, Normal modes and localization in nonlinear systems, Wiley Interscience, New-York, 1996.
[5] A. F. Vakakis Non linear normal modes (NNMs) and their applications in vibration theory: an overview. Mechanical Systems and Signal Processing, 11(1), 3-22, 1997.
[6] R. Arquier, S. Bellizzi, R. Bouc, B. Cochelin « Two methods for the computation of non linear modes of vibrating systems at larges amplitudes » Computers and Structures, 84, 1565-1576, 2006.
[7] J-J. Sinou, F. Thouverez, and L. Jézéquel, Methods to Reduce Non-Linear Mechanical Systems for Instability Computation, Archives of Computational Methods in Engineering: State of the Art Reviews, 11(3), 257-344, 2004.
[8] J.-J. Sinou, F. Thouverez and L. Jézéquel, Application of a nonlinear modal instability approach to brake systems, Journal of Vibration and Acoustics 126 (1), 101-107, 2004.
[9] J-J. Sinou , F. Thouverez and L. Jézéquel, Stability analysis and non-linear behaviour of structural systems using the complex non-linear modal analysis, Computers & Structures, 84, 1891-1905, 2006.
[10] C. Touzé, M. Amabili and O. Thomas : Reduced-order models for large-amplitude vibrations of shells including in-plane inertia, Computer Methods in Applied Mechanics and Engineering, vol. 197, No. 21-24, pp. 2030-2045, 2008.
[11] M. Amabili and C. Touzé : Reduced-order models for non-linear vibrations of fluid-filled circular cylindrical shells: comparison of POD and asymptotic non-linear normal modes methods, Journal of Fluids and Structures, vol. 23, No. 6, pp. 885-903, 2007.
[12] C. Touzé and M. Amabili : Non-linear normal modes for damped geometrically non-linear systems: application to reduced-order modeling of harmonically forced structures, Journal of Sound and Vibration, vol. 298, No. 4-5, pp. 958-981, 2006.
[13]C. Touzé, O.Thomas and A. Huberdeau : Asymptotic non-linear normal modes for large-amplitude vibrations of continuous structures, Computers and Structures, Vol 82, No 31-32, pp 2671-2682, 2004.
[14] C. Touzé, O.Thomas and A. Chaigne : Hardening/softening behaviour in non-linear oscillations of structural systems using non-linear normal modes , Journal of Sound and Vibration, vol 273, No 1-2, pp 77-101, 2004.
[15] G. Kerschen, M. Peeters, J.C. Golinval, A.F. Vakakis, Nonlinear normal modes, Part I : A useful framework for the structural dynamicist, Mechanical systems and Signal Processing, 23, 170-194 (2009).
[16] O. Gendelman, L.I. Manevitch, A. F. Vakakis, R. M. Closkey . Energy pumping in non linear mechanical oscillators, Part I : Dynamics of the underlying Hamiltonian systems, Journal of Applied Mechanics, 68(1), 34-42, 2001.
[17] A.F. Vakakis, O. Gendelman, Energy pumping in non linear mechanical oscillators, Part II: Resonance capture, Journal of Applied Mechanics, 68 (1), 42-48, 2001.
[18] A. F. Vakakis, Inducing passive nonlinear energy sinks in vibrating systems, Journal of Vibration and Acoustic, 123, 324-332, 2001.
[19] O. V. Gendelman, Transition of Energy to Nonlinear Localized Mode in Highly Asymmetric System of Nonlinear Oscillators. Nonlinear Dynamics, vol. 25, 237-253, 2001.
[20] Jang Xiaoai, M. MacFarland, L.A. Bergman, A.F. Vakakis, Steady state passive nonlinear energy pumping in coupled oscillators: Theoretical and experimental results, Nonlinear Dynamics, 33, 87-102, 2003.
[21] O.V. Gendelman, Bifurcations of nonlinear normal modes of linear oscillator with strongly nonlinear damped attachment, Nonlinear Dynamics, 37 (2), 115-128, 2004.
[22] O.V. Gendelman, C.-H. Lamarque, Dynamics of linear oscillator coupled to strongly nonlinear attachment with multiple states of equilibrium, Chaos, Solitons & Fractals, 24 (2005) 501-509.
[23] E. Gourdon, C. H. Lamarque Energy Pumping with various nonlinear structures : numerical evidences, Non linear Dynamics, 40(3), 281-307, 2005.
[24] E. Gourdon, C. H. Lamarque, Energy Pumping for a larger span of energy, Journal of Sound and Vibration, 285 (2005) 711-720.
[25] D.M. Mc Farland, L.A Bergman, A. F. Vakakis, Experimental study of non linear energy pumping occuring at a single fast frequency, International Journal of Non linear Mechanics, 40(6), 891-899, 2005.
[26] O.V. Gendelman, E. Gourdon, C.H. Lamarque, Quasiperiodic Energy Pumping in coupled Oscillators under Periodic Forcing, Journal of Sound and Vibration, 294, 651-662, 2006. [27] E. Gourdon, C.H. Lamarque, Nonlinear Energy Sink with Uncertain Parameters, Journal of Computational and Nonlinear Dynamics, July 2006, volume 1, Issue 3, 187-195.
[28] A.I. Musienko, C.-H. Lamarque, L.I. Manevitch, Design of Mechanical Energy Pumping Devices, Journal of Vibration and Control, Vol. 12, No. 4, 355-371 (2006).
[29] Gourdon, E., Alexander, N.A., Taylor, C., Lamarque, C.-H., Pernot, S., Nonlinear energy pumping under transient forcing with strongly nonlinear coupling: Theoretical andexperimental results, J. of Sound and Vibration, 300(3-5), 522-551, 2007.
[30] Manevitch, L.I., Gourdon, E., Lamarque, C.-H., Parameters optimization for energy pumping in strongly nonhomogeneous 2 dof system, Chaos, Solitons & Fractals, 31(4), 900-911, 2007.
[31] Gourdon, E., Lamarque, C.-H., Pernot, S., Contribution to efficiency of irreversible passive energy pumping with a strong nonlinear attachment, Nonlinear Dynamics, 50(4), 793-808, 2007.
[32] Manevitch, L.I., Musienko, A., Lamarque, C.-H., New analytical approach to energy pumping problem in strongly nonhomogeneous 2 dof systems, Meccanica, vol 42 (1), 77-83, 2007.
[33] Manevitch, L.I., Gourdon, E., Lamarque, C.-H., Toward the design of an optimal energetic sink in a strongly inhomogeneous two-degree-of-freedom system, Journal of Applied Mechanics, vol. 74, 1078-1086, 2007.
[34] O.V. Gendelman, Y. Starosvetsky, Quasiperiodic response regimes of linear oscillator coupled to nonlinear energy sink under periodic forcing, American Society of Mechanical Engineers. Transactions of the ASME. Journal of Applied Mechanics, 74, 2, 325-331, 2007.
[35] A.F. Vakakis, O. Gendelman, L.A. Bergman, D.M. McFarland, G. Kerschen, Y. Sup Lee, “Nonlinear Targeted Energy Transfer in Mechanical and Structural Systems I”, Springer, 2009.
[36] A. F. Vakakis, O. V. Gendelman, L. A. Bergman, D. M. McFarland , G. Kerschen, Y. Sup Lee, “Nonlinear Targeted Energy Transfer in Mechanical and Structural Systems II”, Springer, 2009.
[37] D. Laxalde, F. Thouverez, J.J. Sinou, Dynamics of a linear oscillator connected to a small strongly non-linear hysteretic absorber, International Journal of Non-Linear Mechanics, 41, 969-978, 2006.
[38] O. Gendelman, Targeted energy transfer in systems with non-polynomial nonlinearity, Journal of Sound and Vibration, 315 (2008), 732-745.
[39] F. Schmidt, C.-H. Lamarque, Energy pumping for mechanical systems involving non-smooth Saint-Venant terms, International Journal of Nonlinear Mechanics. doi:10.1016/j.ijnonlinmec.2009.11.018
[40] J. Awrejcewicz & C.-H. Lamarque, Bifurcation and chaos in nonsmooth mechanical systems. Vol. Series A. New Jersey, London, Singapore: World Scientific, 543 p., 2003.
[41] Jérôme Bastien, Guilhem Michon , Lionel Manin et Régis Dufour. An analysis of the modified Dahl and Masing models: Application to a belt tensioner. Journal of Sound and Vibration 302 (2007), no. 4-5, 841--864. [42] N. Challamel, Dynamic analysis of elastoplastic shakedown of structures, Int. J. Structural Stability and Dynamics, 5, 2, 259-278, 2005.
[43] N. Challamel, G. Gilles, Stability and dynamics of a plastic softening oscillator, Journal of Sound and Vibration, 301, 608-634, 2007.
[44] Lee, Y. S., F. Nucera, A. F. Vakakis, D. M. McFarland, and L. A. Bergman, "Periodic Orbits, Damped Transitions and Targeted Energy Transfers in Oscillators with Vibro-Impact Attachments," Physica D, Vol. 238, No. 18, pp. 1868-1896, doi:10.1016/j.physd.2009.06.013, 2009.
[45] Viguie, R., G. Kerschen, J. C. Golinval, D. M. McFarland, L. A. Bergman, A. F. Vakakis, and N. van de Wouw, “Using Passive Nonlinear Targeted Energy Transfer to Stabilize Drill-String Systems,” Journal of Mechanical Systems and Signal Processing (Special Issue on ‘Nonlinear Structural Dynamics’), 23:1, pp. 148-169, 2009.
[46] P. Argoul, T.P. Le, Instantaneous indicators of structural behaviour based on the continuous Cauchy wavelet analysis, Mechanical Systems and Signal Processing, Vol. 17, Issue 1, 243-250, 2003.
[47] T-P. Le, P. Argoul, 2004. Continuous wavelet transform for modal identification using free decay response, Journal of Sound and Vibration, Vol 277, pp. 73-100.
[48] T.A. Nguyen, Etude du comportement dynamique et optimisation d’absorbeurs non linéaires : théorie et expérience, Thèse de Doctorat, ENTPE et Ecole Centrale de Lyon, 2010. Numéro d’ordre : 2010-03.
[49] S. Marchesiello, S. Bedaoui, L. Garibaldi, P. Argoul, 2009. Time-dependent identification of a bridge-like structure with crossing loads, Mechanical Systems and Signal Processing, 23 (6), 2009, 2019-2028.
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[51]D. Laxalde, F. Thouverez, J.-J. Sinou, J.-P. Lombard, and S. Baumhauer, Mistuning Identification and Model Updating of an Industrial Blisk., International Journal of Rotating Machinery, vol. 2007, Article ID 17289, 1-10, 2007.
[52] A. Chaigne, C. Touzé and O. Thomas: Nonlinear vibrations and chaos in gongs and cymbals , Acoustical Science and Technology, Acoust. Soc. of Japan, vol. 26, No. 5, pp 403-409, 2005.
[53] O. Cadot, A. Boudaoud and C. Touzé : Statistics of power injection in a plate set into chaotic vibration, Eur. Phys. J. B, vol. 66, pp. 399-407, 2008.
[54] A. Boudaoud, O. Cadot, B. Odille and C. Touzé : Observation of wave turbulence in vibrating plates, Physical Review Letters, vol. 100, 234504, 2008.
[55] C. Touzé and A. Chaigne : Lyapunov exponents from experimental time series. Application to cymbal vibrations , Acta Acustica, vol 86, No 3, pp. 557-567, 2000.
[56] M.A. Boiron, Modélisation phénoménologique de systèmes complexes non linéaires à partir de séries chronologiques scalaires Thèse de doctorat, Mécanique, ENTPE / Université Claude Bernard Lyon 1, 2005.
[57] J.M. Malasoma, New Lorenz-Like chaotic flows with minimal algebraic structure, Indian Journal of Industrial and Applied Mathematics, Vol.1 (2), pp.1-16, 2008.
[58] J.M. Malasoma, Non-chaotic behaviour for a class of quadratic jerk equation, Chaos, Solitons & Fractals, Vol.39 (2), pp.533-539, 2008.
[59] D. Sengelin-Lejri, Reconstruction phénoménologique de systèmes complexes forcés, Thèse de doctorat, ENTPE, Université Claude Bernard Lyon 1, 165p., 2008.
[60] D. Laxalde, F. Thouverez, and J.P. Lombard, Forced Response Analysis of Integrally Bladed Disks With Friction Ring Dampers, J. Vib. Acoust. -- February 2010 -- Volume 132, Issue 1, 011013 (9 pages)
[61] D. Laxalde, F. Thouverez, J.-J. Sinou and J.-P. Lombard, Qualitative Analysis of Forced Response of Blisks with Friction Ring Dampers, European Journal of Mechanics A/Solids, 26(4), 676-687, 2007.
[62] J-J. Sinou, O. Dereure, G-B. Mazet, F. Thouverez and L. Jézéquel, Friction Induced Vibration for an Aircraft Brake System. Part I : Experimental approach and Stability Analysis, International Journal of Mechanical Sciences, 48(2006), 536–554, 2006.
[63] J-J. Sinou, F. Thouverez, L. Jézéquel, O. Dereure and G-B. Mazet, Friction Induced Vibration for an Aircraft Brake System. Part II : Non-Linear Dynamics, International Journal of Mechanical Sciences, 48(2006), 555–567, 2006.
[64] O. Thomas, C. Touzé and E. Luminais : Non-linear vibrations of free-edge thin spherical shells: experiments on a 1:1:2 internal resonance, Nonlinear Dynamics, vol. 49, No. 1-2, pp. 259-284, 2007.
[65] D. Laxalde, F. Thouverez and J.-J. Sinou, Dynamics of linear oscillator connected to a small strongly non-linear hysteretic absorber, International Journal of Non-Linear Mechanics, 41(8), 969-978, 2006.
[66] M. Guskov, J-J. Sinou and F. Thouverez, Multi-dimensional harmonic balance applied to rotor dynamics, Mechanics Research Communications, 35, 537–545, 2008.
[67] N. Lesaffre, J-J. Sinou and F. Thouverez, Contact Analysis of a Flexible Bladed-Rotor, European Journal of Mechanics - A/Solids, 26(3), 541-557, 2007.
[68] P. Saad, A. Al Majid, F. Thouverez and R. Dufour, Equivalent rheological and restoring force models for predicting the harmonic response of elastomer specimens, Journal of Sound and Vibration, 290(3-5), p 619-639
[69] J-J. Sinou, F. Thouverez, and L. Jézéquel, Stability and Non-linear Analysis of a Complex Rotor/Stator Contact, Journal of Sound and Vibration, 278(4-5), 1095-1129, 2004.
[70] C. Camier, C. Touzé and O. Thomas : Non-linear vibrations of imperfect free-edge circular plates and shells, Eur. J. Mechanics, A/solids, vol. 28(3), pp. 500-515, 2009.
[71] C. Touzé, C. Camier, G. Favraud and O. Thomas : Effect of imperfections and damping on the type of non-linearity of circular plates and shallow spherical shells, Mathematical problems in Engineering, vol. 2008, Article ID 678307, 19 pages, doi:10.1155/2008/678307, 2008.
[72] C. Touzé and O.Thomas : Non-linear behaviour of free-edge shallow spherical shells: Effect of the geometry , International Journal of non-linear Mechanics, vol. 41, No. 5, pp. 678-692, 2006.
[73] O.Thomas, C. Touzé and A. Chaigne : Non-linear vibrations of free-edge thin spherical shells: modal interaction rules and 1:1:2 internal resonance , International Journal of Solids and Structures, vol. 42, No. 11-12, pp 3339-3373, 2005.
[74] O.Thomas, C. Touzé and A. Chaigne : Asymmetric non-linear forced vibrations of free-edge circular plates, part II: experiments , Journal of Sound and Vibration, vol 265, No 5, pp. 1075-1101, 2003.
[75] C. Touzé, O.Thomas and A. Chaigne : Asymmetric non-linear forced vibrations of free-edge circular plates, part I: theory , Journal of Sound and Vibration, vol 258, No 4, pp. 649-676, 2002.
[76] Berlioz, A., & Lamarque, C.H., A non-linear model for the dynamics of an inclined cable, Journal of Sound and Vibration, Vol. 279, n° 3-5, p. 619-639, 2005.
[77] Berlioz, A. & Lamarque, C. H., Nonlinear vibrations of an inclined cable, Journal of Vibration and Acoustics, vol. 127, n° 4, p. 315-323, 2005.
[78] Driot, N., Lamarque, C. H., & Berlioz, A., Theoretical and experimental analysis of a base excited rotor, ASME Journal of Computational and Nonlinear Dynamics, vol. 1, n° 4, p. 257-263, 2006.
[79] A. Al Majid, R. Dufour, Energy and damping in an SDOF system subjected to a variable forcing frequency, Journal of Sound and Vibration, Volume 270, Issues 4-5, 5 March 2004, Pages 833-845
[80] A. AlMajid, R. Dufour, Harmonic response of a structure mounted on an isolator modelled with a hysteretic operator : Experiments and prediction, Journal of Sound and Vibration, 277 (1-2), 391-403, 2004.
[81] Remond D., Neyrand J., Aridon G., Dufour R., On the improved use of Chebyshev expansion for mechanical system identification, Mechanical Systems and Signal Processing, 22 (2), 390-407, 2008.
[82] Michon G., Manin L., Remond D., Dufour R., Parker R. G., Parametric Instability of an Axially Moving Belt Subjected to Multifrequency Excitations: Experiments and Analytical Validation, Journal of Applied Mechanics, 75, 041004, 2008.
[83] Michon G., Manin L., Parker R. G., Dufour R., Duffing Oscillator With Parametric Excitation: Analytical and Experimental Investigation on a Belt-Pulley System, Journal of Computational and Nonlinear Dynamics , 3, 031001, (2008)
[84] G. Michon, L. Manin, R. Dufour, Hysteretic behavior of a belt tensioner : Modelling and experimental investigation, Journal of Vibration and Control, vol. 11 (9), 1147-1158, 2005.
[85] A. Al Majid, R. Dufour, Damping in High Transient Motion, Journal of Vibration and Acoustics, 125, 223 (2003).
[86] A. Al Majid, A. Allezy, R. Dufour, Metric damping of MDOF Systems in High Transient Motion, Journal of Vibration and Acoustics, 128, 50 (2008).
[87] N. Kacem, J. Arcamone,, F. Perez-Murano and S. Hentz, Dynamic range enhancement of nonlinear nanomechanical resonant cantilevers for highly sensitive NEMS gas/mass sensor applications”, J. Micromech. Microeng. 20: 045023, 2010
[88] N Kacem, S Hentz, D Pinto, B Reig and V Nguyen, Nonlinear dynamics of nanomechanical beam resonators: improving the performance of NEMS-based sensors, Nanotechnology 20: 275501, 2009
[89] N. Kacem, S. Hentz, Bifurcation topology tuning of a mixed behavior in nonlinear micromechanical resonators, Applied Physics Letters, 95: 183104, 2009
[90] Kacem N., Nonlinear dynamics of M&NEMS resonant sensors : design strategies for performance enhancement, PhD thesis, 2010, INSA de Lyon and CEA LETI, co-advising: R. Dufour, S. Hentz, S. Baguet.
[91] C.-H. Lamarque, S. Pernot and A. Cuer, Damping identification in multi-degree-of-freedom systems via a wavelet-logarithmic decerement, part 1 : Theory, Journal of Sound and Vibration, Volume 235, Issue 3, 17 August 2000, Pages 361-374
[92] S. Erlicher, P. Argoul, 2007. Modal identification of linear non-proportionally damped systems by wavelet transform, Mechanical Systems and Signal Processing, Vol. 21, Issue 3, pp. 1386-1421.
[93] R. Bellet, B. Cochelin, P. Herzog, P.-O. Mattei, Experimental Study of Targeted Energy Transfer from an Acoustic System to a Nonlinear Membrane Absorber, Journal of Sound and Vibration (2010), doi:10.1016/j.jsv.2010.01.029.
[94] B. Cochelin, N. Damil, M. Potier-Ferry, Méthode asymptotique numérique, Hermès – Lavoisier, 2007, 298 pages, ISBN10 : 2-7462-1567-5 [95] S. Bellizzi, R. Sampaio, Smooth Karhunen-Loeve decomposition to analyze randomly vibrating systems, Journal of Sound and Vibration, 325 (3), 491-498, 2009.
[96] S. Bellizzi, R. Bouc, An amplitude phase formulation for nonlinear modes and limit cycles analysis through invariant manifolds, Journal of Sound and Vibration, 300 (3-5), 896-915, 2007.
[97] S. Bellizzi, R. Sampaio, POMs analysis obtained from Karhunen-Loève expansion for randomly vibrating systems, Journal of Sound and Vibration, 297 (3-5), 774-793, 2006.
[98] S. Bellizzi, R. Bouc, M. Defilippi, Une méthode fréquentielle pour l’identification de structures non linéaires, Mécanique et Industries 5, 61-69, 2004.
[99] S. Bellizzi, M. Defilippi, Nonlinear mechanical systems identification using linear systems with random parameters, Mechanical systems and signal processing 17 (1), 203-210, 2003.
[100] B. Cochelin, C. Vergez, A high order purely frequency-based harmonic balance formulation for continuation of periodic solutions, Journal of Sound and Vibration, 324 (1-2), 243-262, 2009. [101] B. Cochelin, P. Herzog, P.O. Mattei, Experimental evidence of energy pumping in acoustics, Comptes Rendus Mécanqiue 334, 11 (2006) 639-644.
[2] L. Jézéquel, C.H. Lamarque. Analysis of non linear dynamical systems by the normal form theory. Journal of Sound and Vibrations, 149(3), 429-459, 1991.
[3] S.W. Shaw, C. Pierre, Non linear normal modes for non linear vibratory systems, Journal of Sound and Vibrations, 164(1), 85-124, 1993.
[4] A.F. Vakakis, L.I. Manevitch, Yu.V. Mikhlin, V.N. Pilipchuk, A.A. Zevin, Normal modes and localization in nonlinear systems, Wiley Interscience, New-York, 1996.
[5] A. F. Vakakis Non linear normal modes (NNMs) and their applications in vibration theory: an overview. Mechanical Systems and Signal Processing, 11(1), 3-22, 1997.
[6] R. Arquier, S. Bellizzi, R. Bouc, B. Cochelin « Two methods for the computation of non linear modes of vibrating systems at larges amplitudes » Computers and Structures, 84, 1565-1576, 2006.
[7] J-J. Sinou, F. Thouverez, and L. Jézéquel, Methods to Reduce Non-Linear Mechanical Systems for Instability Computation, Archives of Computational Methods in Engineering: State of the Art Reviews, 11(3), 257-344, 2004.
[8] J.-J. Sinou, F. Thouverez and L. Jézéquel, Application of a nonlinear modal instability approach to brake systems, Journal of Vibration and Acoustics 126 (1), 101-107, 2004.
[9] J-J. Sinou , F. Thouverez and L. Jézéquel, Stability analysis and non-linear behaviour of structural systems using the complex non-linear modal analysis, Computers & Structures, 84, 1891-1905, 2006.
[10] C. Touzé, M. Amabili and O. Thomas : Reduced-order models for large-amplitude vibrations of shells including in-plane inertia, Computer Methods in Applied Mechanics and Engineering, vol. 197, No. 21-24, pp. 2030-2045, 2008.
[11] M. Amabili and C. Touzé : Reduced-order models for non-linear vibrations of fluid-filled circular cylindrical shells: comparison of POD and asymptotic non-linear normal modes methods, Journal of Fluids and Structures, vol. 23, No. 6, pp. 885-903, 2007.
[12] C. Touzé and M. Amabili : Non-linear normal modes for damped geometrically non-linear systems: application to reduced-order modeling of harmonically forced structures, Journal of Sound and Vibration, vol. 298, No. 4-5, pp. 958-981, 2006.
[13]C. Touzé, O.Thomas and A. Huberdeau : Asymptotic non-linear normal modes for large-amplitude vibrations of continuous structures, Computers and Structures, Vol 82, No 31-32, pp 2671-2682, 2004.
[14] C. Touzé, O.Thomas and A. Chaigne : Hardening/softening behaviour in non-linear oscillations of structural systems using non-linear normal modes , Journal of Sound and Vibration, vol 273, No 1-2, pp 77-101, 2004.
[15] G. Kerschen, M. Peeters, J.C. Golinval, A.F. Vakakis, Nonlinear normal modes, Part I : A useful framework for the structural dynamicist, Mechanical systems and Signal Processing, 23, 170-194 (2009).
[16] O. Gendelman, L.I. Manevitch, A. F. Vakakis, R. M. Closkey . Energy pumping in non linear mechanical oscillators, Part I : Dynamics of the underlying Hamiltonian systems, Journal of Applied Mechanics, 68(1), 34-42, 2001.
[17] A.F. Vakakis, O. Gendelman, Energy pumping in non linear mechanical oscillators, Part II: Resonance capture, Journal of Applied Mechanics, 68 (1), 42-48, 2001.
[18] A. F. Vakakis, Inducing passive nonlinear energy sinks in vibrating systems, Journal of Vibration and Acoustic, 123, 324-332, 2001.
[19] O. V. Gendelman, Transition of Energy to Nonlinear Localized Mode in Highly Asymmetric System of Nonlinear Oscillators. Nonlinear Dynamics, vol. 25, 237-253, 2001.
[20] Jang Xiaoai, M. MacFarland, L.A. Bergman, A.F. Vakakis, Steady state passive nonlinear energy pumping in coupled oscillators: Theoretical and experimental results, Nonlinear Dynamics, 33, 87-102, 2003.
[21] O.V. Gendelman, Bifurcations of nonlinear normal modes of linear oscillator with strongly nonlinear damped attachment, Nonlinear Dynamics, 37 (2), 115-128, 2004.
[22] O.V. Gendelman, C.-H. Lamarque, Dynamics of linear oscillator coupled to strongly nonlinear attachment with multiple states of equilibrium, Chaos, Solitons & Fractals, 24 (2005) 501-509.
[23] E. Gourdon, C. H. Lamarque Energy Pumping with various nonlinear structures : numerical evidences, Non linear Dynamics, 40(3), 281-307, 2005.
[24] E. Gourdon, C. H. Lamarque, Energy Pumping for a larger span of energy, Journal of Sound and Vibration, 285 (2005) 711-720.
[25] D.M. Mc Farland, L.A Bergman, A. F. Vakakis, Experimental study of non linear energy pumping occuring at a single fast frequency, International Journal of Non linear Mechanics, 40(6), 891-899, 2005.
[26] O.V. Gendelman, E. Gourdon, C.H. Lamarque, Quasiperiodic Energy Pumping in coupled Oscillators under Periodic Forcing, Journal of Sound and Vibration, 294, 651-662, 2006. [27] E. Gourdon, C.H. Lamarque, Nonlinear Energy Sink with Uncertain Parameters, Journal of Computational and Nonlinear Dynamics, July 2006, volume 1, Issue 3, 187-195.
[28] A.I. Musienko, C.-H. Lamarque, L.I. Manevitch, Design of Mechanical Energy Pumping Devices, Journal of Vibration and Control, Vol. 12, No. 4, 355-371 (2006).
[29] Gourdon, E., Alexander, N.A., Taylor, C., Lamarque, C.-H., Pernot, S., Nonlinear energy pumping under transient forcing with strongly nonlinear coupling: Theoretical andexperimental results, J. of Sound and Vibration, 300(3-5), 522-551, 2007.
[30] Manevitch, L.I., Gourdon, E., Lamarque, C.-H., Parameters optimization for energy pumping in strongly nonhomogeneous 2 dof system, Chaos, Solitons & Fractals, 31(4), 900-911, 2007.
[31] Gourdon, E., Lamarque, C.-H., Pernot, S., Contribution to efficiency of irreversible passive energy pumping with a strong nonlinear attachment, Nonlinear Dynamics, 50(4), 793-808, 2007.
[32] Manevitch, L.I., Musienko, A., Lamarque, C.-H., New analytical approach to energy pumping problem in strongly nonhomogeneous 2 dof systems, Meccanica, vol 42 (1), 77-83, 2007.
[33] Manevitch, L.I., Gourdon, E., Lamarque, C.-H., Toward the design of an optimal energetic sink in a strongly inhomogeneous two-degree-of-freedom system, Journal of Applied Mechanics, vol. 74, 1078-1086, 2007.
[34] O.V. Gendelman, Y. Starosvetsky, Quasiperiodic response regimes of linear oscillator coupled to nonlinear energy sink under periodic forcing, American Society of Mechanical Engineers. Transactions of the ASME. Journal of Applied Mechanics, 74, 2, 325-331, 2007.
[35] A.F. Vakakis, O. Gendelman, L.A. Bergman, D.M. McFarland, G. Kerschen, Y. Sup Lee, “Nonlinear Targeted Energy Transfer in Mechanical and Structural Systems I”, Springer, 2009.
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Rapport N°1 - date :