[en] The nonlinear tuned vibration absorber (NLTVA) is a recently developed nonlinear absorber which generalizes Den Hartog׳s equal peak method to nonlinear systems. If the purposeful introduction of nonlinearity can enhance system performance, it can also give rise to adverse dynamical phenomena, including detached resonance curves and quasiperiodic regimes of motion. Through the combination of numerical continuation of periodic solutions, bifurcation detection and tracking, and global analysis, the present study identifies boundaries in the NLTVA parameter space delimiting safe, unsafe and unacceptable operations. The sensitivity of these boundaries to uncertainty in the NLTVA parameters is also investigated.
Disciplines :
Aerospace & aeronautics engineering
Author, co-author :
Detroux, Thibaut ; Université de Liège > Département d'aérospatiale et mécanique > Laboratoire de structures et systèmes spatiaux
Habib, Giuseppe ; Université de Liège > Département d'aérospatiale et mécanique > Laboratoire de structures et systèmes spatiaux
Masset, Luc ; Université de Liège > Département d'aérospatiale et mécanique > Laboratoire de structures et systèmes spatiaux
Kerschen, Gaëtan ; Université de Liège > Département d'aérospatiale et mécanique > Laboratoire de structures et systèmes spatiaux
Language :
English
Title :
Performance, robustness and sensitivity analysis of the nonlinear tuned vibration absorber
N. Boechler, G. Theocharis, and C. Daraio Bifurcation-based acoustic switching and rectification Nat. Mater. 10 2011 665 668
D. Antonio, D.H. Zanette, and D. Lopez Frequency stabilization in nonlinear mechanical oscillators Nat. Commun. 3 2012 806
B.S. Strachan, S.W. Shaw, and O. Kogan Subharmonic resonance cascades in a class of coupled resonators J. Comput. Nonlinear Dyn. 8 2013 041015
N. Poovarodom, S. Kanchanosot, and P. Warnitchai Application of non-linear multiple tuned mass dampers to suppress man-induced vibrations of a pedestrian bridge Earthq. Eng. Struct. Dyn. 32 2003 1117 1131
N.A. Alexander, and F. Schilder Exploring the performance of a nonlinear tuned mass damper J. Sound Vib. 319 2009 445 462
M. Febbo, and S.P. Machado Nonlinear dynamic vibration absorbers with a saturation J. Sound Vib. 332 2013 1465 1483
N. Carpineto, W. Lacarbonara, and F. Vestroni Hysteretic tuned mass dampers for structural vibration mitigation J. Sound Vib. 333 2014 1302 1318
D.A.W. Barton, S.G. Burrow, and L.R. Clare Energy harvesting from vibrations with a nonlinear oscillator J. Vib. Acoust. 132 2010 021009
D.D. Quinn, A.L. Triplett, A.F. Vakakis, and L.A. Bergman Energy harvesting from impulsive loads using intentional essential nonlinearities J. Vib. Acoust. 133 2011 011004
P.L. Green, K. Worden, K. Atallah, and N.D. Sims The benefits of Duffing-type nonlinearities and electrical optimisation of a mono-stable energy harvester under white Gaussian excitations J. Sound Vib. 331 2012 4504 4517
A. Karami, and D.J. Inman Powering pacemakers from heartbeat vibrations using linear and nonlinear energy harvesting Appl. Phys. Lett. 100 2012 042901
A.F. Vakakis, O. Gendelman, L.A. Bergman, D.M. McFarland, G. Kerschen, Y.S. Lee, Nonlinear Targeted Energy Transfer in Mechanical and Structural Systems, Series: Solid Mechanics and Its Applications, Springer, New York, 156, 2008.
G. Kerschen, J.J. Kowtko, D.M. McFarland, L.A. Bergman, and A.F. Vakakis Theoretical and experimental study of multimodal tet in a system of coupled oscillators Nonlinear Dyn. 47 2007 285 309
G. Kerschen, Y.S. Lee, A.F. Vakakis, D.M. McFarland, and L.A. Bergman Irreversible passive energy transfer in coupled oscillators with essential nonlinearity SIAM J. Appl. Math. 66 2006 648 679
F. Nucera, A.F. Vakakis, D.M. McFarland, L.A. Bergman, and G. Kerschen Targeted energy transfers in vibro-impact oscillators for seismic mitigation Nonlinear Dyn. 50 2007 651 677
S.A. Hubbard, D.M. McFarland, L.A. Bergman, and A.F. Vakakis Targeted energy transfer between a model flexible wing and nonlinear energy sink J. Aircr. 47 2010 1918 1931
B. Vaurigaud, L.I. Manevitch, and C.H. Lamarque Passive control of aeroelastic instability in a long span bridge model prone to coupled flutter using targeted energy transfer J. Sound Vib. 330 2011 2580 2595
R. Bellet, B. Cochelin, P. Herzog, and P.O. Mattei Experimental study of targeted energy transfer from an acoustic system to a nonlinear membrane absorber J. Sound Vib. 329 2010 2768 2791
E. Gourc, S. Seguy, G. Michon, and A. Berlioz Chatter control in turning process with a nonlinear energy sink Adv. Mater. Res. 698 2013 89 98
G. Habib, T. Detroux, R. Viguié, and G. Kerschen Nonlinear generalization of Den Hartogs equal-peak method Mech. Syst. Signal Process. 52-53 2015 17 28
G. Habib, G. Kerschen, Stability and bifurcation analysis of a Van der Pol-Duffing oscillator with a nonlinear tuned vibration absorber, in: European Nonlinear Dynamics Conference, Vienna, Austria, 2014. Available from: http://orbi.ulg.ac.be/handle/2268/167407 .
Y. Starosvetsky, and O.V. Gendelman Response regimes of linear oscillator coupled to nonlinear energy sink with harmonic forcing and frequency detuning J. Sound Vib. 315 2008 746 765
J. Shaw, S.W. Shaw, and A.G. Haddow On the response of the non-linear vibration absorber Int. J. Non-linear Mech. 24 1989 281 293
Y. Starosvetsky, and O.V. Gendelman Vibration absorption in systems with a nonlinear energy sink nonlinear damping J. Sound Vib. 324 2009 916 939
E. Gourc, G. Michon, S. Seguy, and A. Berlioz Experimental investigation and design optimization of targeted energy transfer under periodic forcing J. Vib. Acoust. 136 2014 021021
C. Duan, and R. Singh Isolated sub-harmonic resonance branch in the frequency response of an oscillator with slight asymmetry in the clearance J. Sound Vib. 314 2008 12 18
D. Takacs, G. Stepan, and S.J. Hogan Isolated large amplitude periodic motions of towed rigid wheels Nonlinear Dyn. 52 2008 27 34
A. Grolet, E. Sarrouy, and F. Thouverez Global and bifurcation analysis of a structure with cyclic symmetry Int. J. Non-linear Mech. 46 2011 727 737
T. Asami, and O. Nishihara Closed-form exact solution to H∞ optimization of dynamic vibration absorbers (application to different transfer functions and damping systems) J. Vib. Acoust. 125 2003 398 405
J.P. den Hartog Mechanical Vibrations 1934 McGraw-Hill New York
J.E. Brock A note on the damped vibration absorber J. Appl. Mech. 13 1946 A284
T. Detroux, L. Renson, L. Masset, G. Kerschen, The harmonic balance method for bifurcation analysis nonlinear mechanical systems, in: International Modal Analysis Conference, Orlando, Florida, USA, 2015. Available from: http://orbi.ulg.ac.be/handle/2268/173556 .
V.S. Afraimovich, and L.P. Shilnikov Invariant two-dimensional tori, their breakdown and stochasticity Trans. Am. Math. Soc. 149 1991 201 212
A. Dhooge, W. Govaerts, and Y.U. Kuznetsov MATCONT a MATLAB package for numerical bifurcation analysis of ODEs ACM Trans. Math. Softw. 29 2003 141 164
R.P. Eason, A.J. Dick, and S. Nagaragaiah Numerical investigation of coexisting high and low amplitude responses and safe basin erosion for a coupled linear oscillator and nonlinear absorber system J. Sound Vib. 333 2014 3490 3504
C. Grappasonni, G. Habib, T. Detroux, G. Kerschen, Experimental demonstration of a 3D-printed nonlinear tuned vibration absorber, in: Thirty-third International Modal Analysis Conference, Orlando, USA, 2015. Available from http://orbi.ulg.ac.be//handle/2268/173803
