Application of nonlinear localization to the optimization of a vibration isolation system

Nayfeh, Tariq A.; Emaci, E.; Vakakis, Alexander F.

doi:10.2514/3.13679

Cited by 3 publications

(3 citation statements)

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“…Hence, localised NNMs can be a novel tool for vibration and shock isolation designs of mechanical systems, since a system whose inherent dynamics leads to motion confinement of external disturbances is more amenable to active or passive control than a system with no such dynamical properties. In a recent work [61], non-linear localisation was employed to design and optimise a vibration isolator that suppresses disturbances generated by a spinning momentum flywheel in a spacecraft application; this suppression is achieved in wide frequency ranges.…”

Section: Non-linear Localisation and Motion Confinementmentioning

confidence: 99%

NON-LINEAR NORMAL MODES (NNMs) AND THEIR APPLICATIONS IN VIBRATION THEORY: AN OVERVIEW

Vakakis

1997

Mechanical Systems and Signal Processing

234

137

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The concept of 'non-linear normal mode' (NNM) is discussed. After providing some introductory definitions, the applications of NNMs to vibration theory are considered. In particular, it is shown how this concept can be used to study forced resonances of non-linear systems and non-linear localisation of vibrational energy in symmetric systems. NNMs can provide a valuable tool for understanding certain essentially non-linear dynamic phenomena that have no counterparts in linear theory and that cannot be analysed by conventional linearised methods. Additional applications of NNMs to modal analysis, model reduction, vibration and shock isolation designs, and the theory of non-linear oscillators are also discussed.

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Section: Non-linear Localisation and Motion Confinementmentioning

confidence: 99%

NON-LINEAR NORMAL MODES (NNMs) AND THEIR APPLICATIONS IN VIBRATION THEORY: AN OVERVIEW

Vakakis

1997

Mechanical Systems and Signal Processing

234

137

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“…Axially vibrating beams with or without distributed elastic constraints have been considered in [22,23] by following a stochastic or deterministic approach, respectively. Nonlinear problems have been studied only recently [24,25]; in particular the existence of localized nonlinear normal modes has been proved in [26][27][28]. In [26] it has been observed that the origin of nonlinear mode localization in lumped-mass periodic systems is the dependence of the frequencies of substructures on their vibration amplitude; thus nonlinearities cause mistuning and localization takes place even in perfectly periodic systems.…”

Section: Introductionmentioning

confidence: 99%

Mode Localization in Dynamics and Buckling of Linear Imperfect Continuous Structures

Luongo

2001

Normal Modes and Localization in Nonlinear Systems

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Abstract. Localization phenomena in one-dimensional imperfect continuous structures are analyzed, both in dynamics and buckling. By using simple models, fundamental concepts about localization are introduced and similarities between dynamics and buckling localization are highlighted. In particular, it is shown that strong localization of the normal modes is due to turning points in which purely imaginary characteristic exponents assume a non zero real part; in contrast, if turning points do not occur, only weak localization can exist. The possibility of a disturbance propagating along the structure is also discussed. A perturbation method is then illustrated, which generalizes the classical WKB method; this allows the differential problem to be transformed into a sequence of algebraic problems in which the spatial variable appears as a parameter. Applications of the method are worked out for beams and strings on elastic soil. All these structures are found to have nearly-defective system matrices, so their characteristic exponents are highly sensitive to imperfections.

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“…The LNMs are normalized to be norm-one. Here, two models are illustrated: model (1) and model (7). Since model (1) is simpler than model (7) and there were many results about it in the literatures, "rstly it is reinvestigated in more detail as a comparison.…”

Section: Base Points Via the Lnmsmentioning

confidence: 99%

Effects of Base Points and Normalization Schemes on the Non-Linear Normal Modes of Conservative Systems

Zhang¹

2002

Journal of Sound and Vibration

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Application of nonlinear localization to the optimization of a vibration isolation system

Cited by 3 publications

References 0 publications

NON-LINEAR NORMAL MODES (NNMs) AND THEIR APPLICATIONS IN VIBRATION THEORY: AN OVERVIEW

NON-LINEAR NORMAL MODES (NNMs) AND THEIR APPLICATIONS IN VIBRATION THEORY: AN OVERVIEW

Mode Localization in Dynamics and Buckling of Linear Imperfect Continuous Structures

Effects of Base Points and Normalization Schemes on the Non-Linear Normal Modes of Conservative Systems

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