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

Yekai Sun,Loïc Salles,Alessandra Vizzaccaro,Jie Yuan

doi:10.1007/s11071-021-06567-0

Yekai Sun, Loïc Salles + Show 2 more

Open Access

https://doi.org/10.1007/s11071-021-06567-0

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Abstract

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.

Highlights

To improve the structural design of a future engineering component, various nonlinear characteristics have to be taken into consideration in the dynamic analysis
The definition (2) can be extended to the non-conservative nonlinear systems as the assumption of a periodic orbit is no longer included. Both analytical and numerical methods can be used to compute the Nonlinear normal mode (NNM) based on the definition (2), where analytical methods are usually based on polynomial series expansions to parametrise the geometry of the manifold [28], whereas numerical methods rely on computing the solution of the partial differential equations that govern the manifold [22]
According to [14], the full forced response is synthesised by a single nonlinear mode and other linearised modes, whereas the present study focuses on the prediction of the resonant solution

Summary

Introduction

To improve the structural design of a future engineering component, various nonlinear characteristics have to be taken into consideration in the dynamic analysis. The existence of nonlinear damping terms makes the autonomous system non-conservative, classic nonlinear modal analysis methods for conservative systems cannot be applied [13]. The definition (2) can be extended to the non-conservative nonlinear systems as the assumption of a periodic orbit is no longer included. Both analytical and numerical methods can be used to compute the NNM based on the definition (2), where analytical methods are usually based on polynomial series expansions to parametrise the geometry of the manifold [28], whereas numerical methods rely on computing the solution of the partial differential equations that govern the manifold [22]

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