Multi-frequency; nonlinear energy transfer; linear oscillators; nonlinear normal modes
Abstract :
[en] We report on multi-frequency energy transfer from a two-mode, initially excited linear system to a multi-degree-of-freedom (mdof) essentially nonlinear attachment. This occurs through simultaneous resonance interactions of both linear modes with a set of nonlinear normal modes (NNMs) of the attachment, and is studied utilizing numerical wavelet transforms. The multi-frequency nonlinear energy transfer discussed herein differs from multi-frequency energy transfer caused by resonance capture cascading where sequential energy transfer from a set of linear modes to single-dof nonlinear attachments takes place. (c) 2004 Elsevier Ltd. All rights reserved.
A.F. Vakakis, L.I. Manevitch, O. Gendelman, and L. Bergman Dynamics of linear discrete systems connected to local essentially nonlinear attachments Journal of Sound and Vibration 264 2003 559 577
D. Quinn, and R.H. Rand The dynamics of resonance capture Nonlinear Dynamics 8 1995 1 20
D. Quinn Resonance capture in a three degree of freedom mechanical system Nonlinear Dynamics 14 1997 309 333
P. Argoul, and T.-P. Le Instantaneous indicators of structural behaviour based on the continuous cauchy wavelet analysis Mechanical Systems and Signal Processing 17 1 2003 243 250
T.-P. Le, and P. Argoul Continuous wavelet tranform for modal identification using free decay response Journal of Sound and Vibration 277 2004 73 100
H.P. Yin, D. Duhamel, and P. Argoul Natural frequencies and damping estimation using wavelet transform of a frequency response function Journal of Sound and Vibration 271 2004 999 1014
P.N. Panagopoulos, A.F. Vakakis, and S. Tsakirtzis Transient resonant interactions of linear chains with essentially nonlinear end attachments leading to passive energy pumping International Journal of Solids and Sructures 41 2004 6505 6528
A.F. Vakakis, L.I. Manevitch, Yu.V. Mikhlin, V.N. Pilipchuk, and A.A. Zevin Normal Modes and Localization in Nonlinear Systems 1996 Wiley New York