Reduced order modeling of blades with geometric nonlinearities and contact interactions

Delhez, Elise; Nyssen, Florence; Golinval, Jean‐Claude; Batailly, Alain

doi:10.1016/j.jsv.2021.116037

Cited by 20 publications

(8 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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“…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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“…These aspects have also been investigated in the more general context of thin and slender structures [26,27,28,29,30,31]. Concerning the context of turbomachines, various research can be found for the deterministic case [32,33,34], but also in presence of contact nonlinearities [35] or in presence of mistuning [36].…”

Section: Introductionmentioning

confidence: 99%

Nonlinear stochastic dynamics of detuned bladed-disks with uncertain mistuning and detuning optimization using a probabilistic machine learning tool

Capiez‐Lernout

Soize

2022

International Journal of Non-Linear Mechanics

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Reduced order modeling of blades with geometric nonlinearities and contact interactions

Cited by 20 publications

References 50 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

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

Nonlinear stochastic dynamics of detuned bladed-disks with uncertain mistuning and detuning optimization using a probabilistic machine learning tool

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