nonlinear energy pumping; multimodal targeted energy transfer; essential nonlinearity; resonance capture; nonlinear beating phenomenon
Abstract :
[en] The purpose of this study is the theoretical and experimental investigation of targeted energy transfers from a two-degree-of-freedom primary structure to a nonlinear energy sink (NES). It is demonstrated that an NES can resonate with and extract energy from both modes of the primary structure. By facilitating these energy transfers, notably through excitation of appropriate periodic and quasi-periodic orbits, one can promote dissipation of a major portion of externally induced energy in the nonlinear attachment.
Disciplines :
Mechanical engineering Physics
Author, co-author :
Kerschen, Gaëtan ; Université de Liège - ULiège > Département d'aérospatiale et mécanique > Laboratoire de structures et systèmes spatiaux
Kowtko, Jeffrey J.; University of Illinois at Urbana-Champaign (U.S.A.) > Department of Aerospace Engineering
McFarland, D. Michael; University of Illinois at Urbana-Champaign (U.S.A.) > Department of Aerospace Engineering
Bergman, Lawrence A.; University of Illinois at Urbana-Champaign (U.S.A.) > Department of Aerospace Engineering
Vakakis, Alexander F.; National Technical University of Athens (Greece) > Division of Mechanics
Language :
English
Title :
Theoretical and experimental study of multimodal targeted energy transfer in a system of coupled oscillators
Frahm, H.: A device for damping vibrations of bodies. US Patent 989958, (1911)
Den Hartog, J.P.: Mechanical vibration, McGraw-Hill, New York (1947)
Xu, K., Igusa, T.: Dynamic characteristics of multiple substructures with closely spaced frequencies. Earthquake Eng. Struct. Dyn. 21, 1059-1070 (1992)
Abe, M., Fujino, Y.: Dynamic characterization of multiple tuned mass dampers and some design. Earthquake Eng. Struct. Dyn. 23, 813-835 (1994)
Kitis, L., Wang, B.P., Pilkey, W.D.: Vibration reduction over a frequency range. J. Sound Vib. 89, 559-569 (1983)
Zuo, L., Nayfeh, S.A.: Minimax optimization of multi-degree-of-freedom tuned-mass dampers. J. Sound Vib. 272, 893-908 (2004)
Hrovat, D., Barak, P., Rabins, M.: Semi-active versus passive or active tuned mass dampers for structural control. J. Eng. Mech. 109, 691-705 (1983)
Seto, K., Tominari, N.: Effect of a variable stiffness-type dynamic damper on machine tools with long overhung ram. Bull. JSME 19, 1270-1277 (1976)
Chang, J.C.H., Soong, T.T.: Structural control using active tuned mass dampers. J. Eng. Mech. 106, 1091-1098 (1980)
Roberson, R.E.: Synthesis of a nonlinear dynamic vibration absorber. J. Franklin Inst. 254, 205-220 (1952)
Oueini, S.S., Chin, C.M., Nayfeh, A.H.: Dynamics of a cubic nonlinear vibration absorber. Nonlinear Dyn. 20, 283-295 (1999)
Agnes, G.S., Inman, D.J.: Performance of nonlinear vibration absorbers for multi-degree-of-freedom systems using nonlinear normal modes. Nonlinear Dyn. 25, 275-292 (2001)
Vyas, A., Bajaj, A.K., Raman, A.: Dynamics of structures with wideband autoparametric vibration absorbers: theory. In: Proceedings of the Royal Society of London Series A-Mathematical Phys. Eng. Sci. 460, 1547-1581 (2004)
Gendelman, O.: Transition of energy to a nonlinear localized mode in a highly asymmetric system of two oscillators. Nonlinear Dyn. 25, 237-253 (2001)
Vakakis, A.F., Gendelman, O.: Energy pumping in nonlinear mechanical oscillators: part II - resonance capture. J. Appl. Mech. 68, 42-48 (2001)
Lee, Y.S., Kerschen, G., Vakakis, A.F., Panagopoulos, P., Bergman, L.A., McFarland, D.M.: Complicated dynamics of a linear oscillator with an essentially nonlinear local attachment. Physica D 204, 41-69 (2005)
Kerschen, G., Lee, Y.S., Vakakis, A.F., McFarland, D.M., Bergman, L.A.: Irreversible passive energy transfer in coupled oscillators with essential nonlinearity. SIAM J. Appl. Math. 66, 648-679 (2006)
Panagopoulos,P.,Gendelman, O., Vakakis, A.F.: Robustness of nonlinear targeted energy transfer in coupled oscillators to changes of initial conditions. Nonlinear Dyn. in review. (2005)
McFarland, D.M., Bergman, L.A., Vakakis, A.F.: Experimental study of nonlinear energy pumping occurring at a single fast frequency. Int. J. Nonlinear Mech. 40, 891-899 (2005)
McFarland, D.M., Kerschen, G., Kowtko, J.J., Lee, Y.S., Bergman, L.A., Vakakis, A.F.: Experimental investigation of targeted energy transfers in strongly and nonlinearly coupled oscillators. J. Acoust. Soc. America 118, 791-799 (2005)
Vakakis, A.F., Manevitch, L.I., Gendelman, O., Bergman, L. A. : Dynamics of linear discrete systems connected to local, essentially non-linear attachments. J. Sound Vib. 264, 559-577 (2003)
Vakakis, A.F., McFarland, D.M., Bergman, L.A., Manevitch, L.I., Gendelman, O.: Isolated resonance captures and resonance capture cascades leading to single- or multi-mode passive energy pumping in damped coupled oscillators. J. Vib. Acoust. 126, 235-244 (2004)
Gendelman, O.V.: Bifurcations of nonlinear normal modes of linear oscillator with strongly nonlinear damped attachment. Nonlinear Dyn. 37, 117-125 (2004)
Manevitch, L.I.: 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, pp. 269-300 (1999)
Van Overschee, P., DeMoor, B.: Subspace identification for linear systems: theoiy, implementation, applications, Kluwer Academic Publishers, Boston (1996)
Masri, S.F., Caughey, T.K.: A nonparametric identification technique for nonlinear dynamic systems. J. Appl. Mech. 46, 433-441 (1979)
Mankala, R., Quinn, D.D.: Resonant dynamics and saturation in a coupled system with quadratic nonlinearilles. Proceedings of the ASME-DETC Conference, Anaheim (2004)
