Nonlinear Modes of Vibration and Internal Resonances in Nonlocal Beams

Ribeiro, Pedro; Thomas, Olivier

doi:10.1115/1.4035060

Cited by 16 publications

(4 citation statements)

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“…In this realm, the following directions should be investigated soon as direct applications of the general method. First of all, applications to different physical problems, including different types of nonlinear forces, should be investigated, as for example nonlinear damping laws [5,6,37], coupling with other physical forces such as piezoelectric couplings [68,138,250], piezoelectric material nonlinearities [62,139,299], non-local models for nanostructures [238,239], often used in energy-harvesting problems, electrostatic forces in MEMS dynamics [319], centrifugal and Coriolis effects in rotating systems [44,267] with applications to blades [79,224,226,271], large strain elastic nonlinear constitutive laws [187], fluid-structure interaction [107,165] and coupling with nonlinear aeroelastic forces [48]; or thermal effects [99,219], to cite a few of the most obvious directions where the general reduction strategy could be easily extended. Extensions to structures with symmetries, in order to get more quantitative informations and highlight the link with mode localization, could be also used with such tools [65,291,308,309].…”

Section: Open Problems and Future Directionsmentioning

confidence: 99%

Model order reduction methods for geometrically nonlinear structures: a review of nonlinear techniques

2021

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This paper aims at reviewing nonlinear methods for model order reduction in structures with geometric nonlinearity, with a special emphasis on the techniques based on invariant manifold theory. Nonlinear methods differ from linear-based techniques by their use of a nonlinear mapping instead of adding new vectors to enlarge the projection basis. Invariant manifolds have been first introduced in vibration theory within the context of nonlinear normal modes and have been initially computed from the modal basis, using either a graph representation or a normal form approach to compute mappings and reduced dynamics. These developments are first recalled following a historical perspective, where the main applications were first oriented toward structural models that can be expressed thanks to partial differential equations. They are then replaced in the more general context of the parametrisation of invariant manifold that allows unifying the approaches. Then, the specific case of structures dis-C. Touzé (B)

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Section: Open Problems and Future Directionsmentioning

confidence: 99%

Model order reduction methods for geometrically nonlinear structures: a review of nonlinear techniques

2021

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“…A number of these are devoted to carbon nanotubes. Special attention deserves the works of Ribeiro [13] which attempts to develop a specific finite element model to model the vibration behaviour and to analyse internal resonances of beams with dimensions of a few nanometers. This study uses Bernouli Euler p-version beam elements to model the behaviour of nano-sized beams.…”

Section: Introductionmentioning

confidence: 99%

Vibratory behaviour of glass fibre reinforced polymer (GFRP) interleaved with nylon nanofibers

Garcia¹,

Wilson

Trendafilova³

et al. 2017

Composite Structures

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This version is available at https://strathprints.strath.ac.uk/61788/ Strathprints is designed to allow users to access the research output of the University of Strathclyde. Unless otherwise explicitly stated on the manuscript, Copyright © and Moral Rights for the papers on this site are retained by the individual authors and/or other copyright owners. Please check the manuscript for details of any other licences that may have been applied. You may not engage in further distribution of the material for any profitmaking activities or any commercial gain. You may freely distribute both the url (https://strathprints.strath.ac.uk/) and the content of this paper for research or private study, educational, or not-for-profit purposes without prior permission or charge.Any correspondence concerning this service should be sent to the Strathprints administrator: strathprints@strath.ac.ukThe Strathprints institutional repository (https://strathprints.strath.ac.uk) is a digital archive of University of Strathclyde research outputs. It has been developed to disseminate open access research outputs, expose data about those outputs, and enable the management and persistent access to Strathclyde's intellectual output. 1 Vibratory behaviour of glass fibre reinforced polymer (GFRP) interleaved with Nylon NanofibersCristobal Garcia AbstractThe main purpose of this study is to investigate the influence of the inclusion of nylon nanofibers on the global dynamic behaviour of GFRP composite laminates. The vibration behaviour of GFRP composites reinforced with nylon nano-fibres is considered experimentally and numerically using a finite element model. The present analysis of clamped-clamped beams investigates the natural frequencies, the damping and the stiffness of virgin and nano-interleaved composite laminates. The numerical modelling uses ANSYS Workbench 16.2. Experimental and numerical results showed a significant effect of the nylon nanofibers on the dynamic behaviour of the composites. Nano-modified composites demonstrated a consistent increase in the damping ratio and inter-laminar strength. However, the variation in natural frequencies and stiffness due to the nanofibers was very small. This study contributes to the knowledge about the macro dynamic properties of nylon interleaved GFRP composites. It demonstrates that a simple FE model can be used to accurately predict the dynamic behaviour of such nano-composites.

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“…In this realm, the following directions should be investigated soon as direct applications of the general method. First of all, applications to different physical problems, including different types of nonlinear forces, should be investigated, as for example nonlinear damping laws [5,6,37], coupling with other physical forces such as piezoelectric couplings [66,137,251], piezoelectric material nonlinearities [60,138,299], non-local models for nanostructures [239,240], often used in energy-harvesting problems, electrostatic forces in MEMS dynamics [319], centrifugal and Coriolis effects in rotating systems [44,268] with applications to blades [77,225,227,272], large strain elastic nonlinear constitutive laws [188], fluid-structure interaction [105,166] and coupling with nonlinear aeroelastic forces [46]; or thermal effects [97,220], to cite a few of the most obvious directions where the general reduction strategy could be easily extended. Extensions to structures with symmetries, in order to get more quantitative informations and highlight the link with mode localization could be also used with such tools [63,292,308,309].…”

Section: Open Problems and Future Directionsmentioning

confidence: 99%

Model order reduction methods for geometrically nonlinear structures: a review of nonlinear techniques

Touzé,

Vizzaccaro,

Thomas

2021

Preprint

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This paper aims at reviewing nonlinear methods for model order reduction of structures with geometric nonlinearity, with a special emphasis on the techniques based on invariant manifold theory. Nonlinear methods differ from linear based techniques by their use of a nonlinear mapping instead of adding new vectors to enlarge the projection basis. Invariant manifolds have been first introduced in vibration theory within the context of nonlinear normal modes (NNMs) and have been initially computed from the modal basis, using either a graph representation or a normal form approach to compute mappings and reduced dynamics. These developments are first recalled following a historical perspective, where the main applications were first oriented toward structural models that can be expressed thanks to partial differential equations (PDE). They are then replaced in the more general context of the parametrisation of invariant manifold that allows unifying the approaches. Then the specific case of structures discretized with the finite element method is addressed. Implicit condensation, giving rise to a projection onto a stress manifold, and modal derivatives, used in the framework of the quadratic manifold, are first reviewed. Finally, recent developments allowing direct computation of reduced-order models (ROMs) relying on invariant manifolds theory are detailed. Applicative examples are shown and the extension of the methods to deal with further complications are reviewed. Finally, open problems and future directions are highlighted.

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Nonlinear Modes of Vibration and Internal Resonances in Nonlocal Beams

Cited by 16 publications

References 40 publications

Model order reduction methods for geometrically nonlinear structures: a review of nonlinear techniques

Model order reduction methods for geometrically nonlinear structures: a review of nonlinear techniques

Vibratory behaviour of glass fibre reinforced polymer (GFRP) interleaved with nylon nanofibers

Model order reduction methods for geometrically nonlinear structures: a review of nonlinear techniques

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