Multi-scaled analysis of the damped dynamics of an elastic rod with an essentially nonlinear end attachment

International Journal of Solids and Structures

Volumn 44, Issue 18-19, 2007, Pages 6256-6278

  Panagopoulos, Panayotis ^a   Georgiades, Fotios ^a   Tsakirtzis, Stylianos ^a   Vakakis, Alexander F ^a,b   Bergman, Lawrence A ^b  

^a NATIONAL TECHNICAL UNIVERSITY OF ATHENS   (Greece)

^b University of Illinois at Urbana Champaign   (United States)

Author keywords

Essential nonlinearity; Multi scaled analysis; Nonlinear damped transitions

Indexed keywords

ESSENTIAL NONLINEARITY; FREQUENCY-ENERGY PLOT (FEP); MULTI-SCALED ANALYSIS; NONLINEAR DAMPED TRANSITIONS;

DAMPING; DYNAMICAL SYSTEMS; HAMILTONIANS; HILBERT SPACES; STIFFNESS; VISCOSITY; WAVELET TRANSFORMS;

NONLINEAR SYSTEMS;

EID: 34447515760     PISSN: 00207683     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijsolstr.2007.02.025     Document Type: Article

References (14)

1. Argoul P., and Le T.P. Instantaneous indicators of structural behaviour based on the continuous Cauchy wavelet analysis. Mechanical Systems and Signal Processing 17 1 (2003) 243-250
2. Georgiades, F., Vakakis, A.F., Kerschen, G., in press. Broadband passive targeted energy pumping from a linear dispersive rod to a lightweight essentially nonlinear end attachment, International Journal for Nonlinear Mechanics.
3. Huang N.E., Shen Z., Long S.R., Wu M.C., Shih H.H., Zheng Q., Yen N.C., Tung C.C., and Liu H.H. The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis. Proceedings of the Royal Society of London, Series A 454 (1998) 903-995
4. Huang W., Shen Z., Huang N.E., and Fung Y.C. Engineering analysis of biological variables: an example of blood pressure over 1 day. Proceedings of the National Academy of Sciences 95 (1998) 4816-4821
5. Huang N.E., Shen Z., and Long S.R. A new view of nonlinear water waves: the Hilbert spectrum. Annual Review of Fluid Mechanics 31 (1999) 417-457
6. Huang N.E., Wu M.C., Long S.R., Shen S.S.P., Qu W., Gloersen P., and Fan K.L. A confidence limit for the empirical mode decomposition and Hilbert spectral analysis. Proceedings of the Royal Society of London, Series A 459 (2003) 2317-2345
7. Kerschen G., Sup Lee Y., Vakakis A.F., McFarland D.M., and Bergman L.A. Irreversible passive energy transfer in coupled oscillators with essential nonlinearity. SIAM Journal on Applied Mathematics 66 2 (2006) 648-679
8. Kerschen, G., Vakakis, A.F., Lee, Y.S., McFarland, D.M., Bergman, L.A., 2006b. Toward a fundamental understanding of the Hilbert-Huang transform in nonlinear structural dynamics, in: Proceedings of the 24th International Modal Analysis Conference (IMAC), St. Louis, MO.
9. Kerschen, G., Vakakis, A.F., Lee, Y.S., McFarland, D.M., Bergman, L.A., submitted for publication. Toward a fundamental understanding of the Hilbert-Huang transform in nonlinear structural dynamics, Journal of Vibration and Control.
10. Le T.-P., and Argoul P. Continuous wavelet transform for modal identification using free decay response. Journal of Sound and Vibration 277 (2004) 73-100
11. Lee Y.S., Kerschen G., Vakakis A.F., Panagopoulos P.N., Bergman L.A., and McFarland D.M. Complicated dynamics of a linear oscillator with a light, essentially nonlinear attachment. Physica D 204 1-2 (2005) 41-69
12. Vakakis A.F., Manevitch L.I., Musienko A., Kerschen G., and Bergman L.A. Transient dynamics of a dispersive elastic wave guide weakly coupled to an essentially nonlinear end attachment. Wave Motion 41/2 (2004) 109-132
13. Veltcheva A.D. Wave and group transformation by a Hilbert spectrum. Coastal Engineering Journal 44 4 (2002) 283-300
14. Wu M.L., Schubert S., and Huang N.E. The development of the South Asian summer monsoon and the intraseasonal oscillation. Journal of Climate 12 (1999) 2054-2075