# Nonlinear normal modes, Part I: A useful framework for the structural dynamicist

@inproceedings{Kerschen2009NonlinearNM, title={Nonlinear normal modes, Part I: A useful framework for the structural dynamicist}, author={G. Kerschen and Maxime Peeters and Jean-Claude Golinval and Alexander F. Vakakis}, year={2009} }

The concept of nonlinear normal modes (NNMs) is discussed in the present paper and its companion, Part II. Because there is virtually no application of the NNMs to large-scale engineering structures, these papers are an attempt to highlight several aspects that might drive their development in the future. Specifically, we support that (i) numerical methods for the continuation of periodic solutions pave the way for an effective and practical computation of NNMs, and (ii) time–frequency analysis… CONTINUE READING

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#### References

##### Publications referenced by this paper.

SHOWING 1-10 OF 111 REFERENCES

## On periodic solutions close to rectilinear normal vibration modes: PMM vol. 36, n≗6, 1972, pp. 1051–1058

VIEW 4 EXCERPTS

HIGHLY INFLUENTIAL

## Reduced-order models for large-amplitude vibrations of shells including in-plane inertia

VIEW 4 EXCERPTS

HIGHLY INFLUENTIAL

## A Wavelet Tour of Signal Processing

VIEW 8 EXCERPTS

HIGHLY INFLUENTIAL

## Ground Vibration Testing of Large Aircraft - State-of-the-Art and Future Perspectives

VIEW 3 EXCERPTS

HIGHLY INFLUENTIAL

## Normal modes and localization in nonlinear systems

VIEW 8 EXCERPTS

## On Direct Methods for Constructing Nonlinear Normal Modes of Continuous Systems

VIEW 4 EXCERPTS

HIGHLY INFLUENTIAL

## Practical Bifurcation and Stability Analysis

VIEW 2 EXCERPTS

## AUTO

VIEW 2 EXCERPTS