Comparison of different methodologies for the computation of damped nonlinear normal modes and resonance prediction of systems with non-conservative nonlinearities

The nonlinear modes of a non-conservative nonlinear system are sometimes referred to as damped nonlinear normal modes (dNNMs). Because of the non-conservative characteristics, the dNNMs are no longer periodic. To compute non-periodic dNNMs using classic methods for periodic problems, two concepts ha...

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Bibliographic Details
Published in:Nonlinear dynamics 2021-06, Vol.104 (4), p.3077-3107
Main Authors: Sun, Yekai, Yuan, Jie, Vizzaccaro, Alessandra, Salles, Loïc
Format: Article
Language:English
Subjects:
Automotive Engineering
Classical Mechanics
Control
Damping
Dynamical Systems
Engineering
Mechanical Engineering
Methods
Nonlinear response
Nonlinear systems
Nonlinearity
Numerical analysis
Orbits
Original Paper
Partial differential equations
Vibration
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Summary:The nonlinear modes of a non-conservative nonlinear system are sometimes referred to as damped nonlinear normal modes (dNNMs). Because of the non-conservative characteristics, the dNNMs are no longer periodic. To compute non-periodic dNNMs using classic methods for periodic problems, two concepts have been developed in the last two decades: complex nonlinear mode (CNM) and extended periodic motion concept (EPMC). A critical assessment of these two concepts applied to different types of non-conservative nonlinearities and industrial full-scale structures has not been thoroughly investigated yet. Furthermore, there exist two emerging techniques which aim at predicting the resonant solutions of a nonlinear forced response using the dNNMs: extended energy balance method (E-EBM) and nonlinear modal synthesis (NMS). A detailed assessment between these two techniques has been rarely attempted in the literature. Therefore, in this work, a comprehensive comparison between CNM and EPMC is provided through two illustrative systems and one engineering application. The EPMC with an alternative damping assumption is also derived and compared with the original EPMC and CNM. The advantages and limitations of the CNM and EPMC are critically discussed. In addition, the resonant solutions are predicted based on the dNNMs using both E-EBM and NMS. The accuracies of the predicted resonances are also discussed in detail.
ISSN:0924-090X
1573-269X
DOI:10.1007/s11071-021-06567-0