Localization of vibrations in large space reflectors

Bendiksen, Oddvar O.; Cornwell, Phillip

doi:10.2514/3.10084

Cited by 53 publications

(12 citation statements)

References 12 publications

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“…the one presented in Fig. 1 may be understood as a minimal model of different aerospace structures, such as space reflectors [3], disk antennas [28] and bladeddisks of aero-engines [6,7]. In the case of bladed-disk vibrations, the model presented in Fig.…”

Section: The Model and Solution Methodsmentioning

confidence: 99%

“…Localisation of vibrations has received considerable attention from the structural dynamics engineering community over the last three decades (see e. g. papers [1,2,3,4,5,6,7,8] and references therein). In a linear framework, localisa-tion may arise due to imperfections in the manufacturing process that result in a slightly disordered and inhomogeneous system.…”

Section: Introductionmentioning

confidence: 99%

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Dark solitons, modulation instability and breathers in a chain of weakly nonlinear oscillators with cyclic symmetry

Fontanela

Grolet

Salles

et al. 2018

Journal of Sound and Vibration

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In the aerospace industry the trend for light-weight structures and the resulting complex dynamic behaviours currently challenge vibration engineers. In many cases, these light-weight structures deviate from linear behaviour, and complex nonlinear phenomena can be expected. We consider a cyclically symmetric system of coupled weakly nonlinear undamped oscillators that could be considered a minimal model for different cyclic and symmetric aerospace structures experiencing large deformations. The focus is on localised vibrations that arise from wave envelope modulation of travelling waves. For the defocussing parameter range of the approximative nonlinear evolution equation, we show the possible existence of dark solitons and discuss their characteristics. For the focussing parameter range, we characterise modulation instability and illustrate corresponding nonlinear breather dynamics. Furthermore, we show that for stronger nonlinearity or randomness in initial conditions, transient breather-type dynamics and decay into bright solitons appear. The findings suggest that significant vibration localisation may arise due to mechanisms of nonlinear modulation dynamics.

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Section: The Model and Solution Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Dark solitons, modulation instability and breathers in a chain of weakly nonlinear oscillators with cyclic symmetry

Fontanela

Grolet

Salles

et al. 2018

Journal of Sound and Vibration

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show abstract

“…qualitative changes in system dynamics (see e.g. [19][20][21][22][23][24][25][26][27][28]). Nonlinear localization has been shown to appear not only in conservative systems [19] but also in friction-excited chains of weakly coupled oscillators [20,21], where the authors showed that the localization phenomenon is strongly related to the bistable behaviour of the single oscillator in the chain.…”

Section: Introductionmentioning

confidence: 99%

Multistability and localization in forced cyclic symmetric structures modelled by weakly-coupled Duffing oscillators

Papangelo

Fontanela

Grolet

et al. 2019

Journal of Sound and Vibration

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Many engineering structures are composed of weakly coupled sectors assembled in a cyclic and ideally symmetric configuration, which can be simplified as forced Duffing oscillators. In this paper, we study the emergence of localized states in the weakly nonlinear regime. We show that multiple spatially localized solutions may exist, and the resulting bifurcation diagram strongly resembles the snaking pattern observed in a variety of fields in physics, such as optics and fluid dynamics. Moreover, in the transition from the linear to the nonlinear behaviour isolated branches of solutions are identified. Localization is caused by the hardening effect introduced by the nonlinear stiffness, and occurs at large excitation levels. Contrary to the case of mistuning, the presented localization mechanism is triggered by the nonlinearities and arises in perfectly homogeneous systems.

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“…(39), the forced response in physical coordinates follows from Eq. (57) and is given by q ss ðtÞ ¼ e nþ1 u ss nþ1 ðtÞ (77) where e nþ1 is the ðn þ 1Þth column of the Fourier matrix and u ss nþ1 ðtÞ is given by Eq. (76).…”

Section: Forced Response Of a General Cyclic System Undermentioning

confidence: 99%

Circulant Matrices and Their Application to Vibration Analysis

Olson

Shaw

Shi

et al. 2014

Applied Mechanics Reviews

109

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This paper provides a tutorial and summary of the theory of circulant matrices and their application to the modeling and analysis of the free and forced vibration of mechanical structures with cyclic symmetry. Our presentation of the basic theory is distilled from the classic book of Davis (1979, Circulant Matrices, 2nd ed., Wiley, New York) with results, proofs, and examples geared specifically to vibration applications. Our aim is to collect the most relevant results of the existing theory in a single paper, couch the mathematics in a form that is accessible to the vibrations analyst, and provide examples to highlight key concepts. A nonexhaustive survey of the relevant literature is also included, which can be used for further examples and to point the reader to important extensions, applications, and generalizations of the theory.

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Localization of vibrations in large space reflectors

Cited by 53 publications

References 12 publications

Dark solitons, modulation instability and breathers in a chain of weakly nonlinear oscillators with cyclic symmetry

Dark solitons, modulation instability and breathers in a chain of weakly nonlinear oscillators with cyclic symmetry

Multistability and localization in forced cyclic symmetric structures modelled by weakly-coupled Duffing oscillators

Circulant Matrices and Their Application to Vibration Analysis

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