The transverse vibration of a rotating beam with tip mass: The method of integral equations

Jones, Louise H.

doi:10.1090/qam/99665

Cited by 18 publications

(11 citation statements)

References 6 publications

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“…This effect is addressed in [77] with a standard Euler-Bernoulli model and in [12] with a Timoshenko model. The effect of various parameters on the natural frequencies of rotating beams has also been widely studied: the effect of variable and non-symmetrical cross sections, pre-twist [60,63], precone, pre-lag, setting angle [11,44], root offset [14,43], taper and rotary inertia, attached masses [5,38,57], shrouds, springs [22] and various boundary conditions [10]. The finite-element method has also been used widely used: see, i.e., [8] and the textbook [32].…”

Section: Introductionmentioning

confidence: 99%

Hardening/softening behavior and reduced order modeling of nonlinear vibrations of rotating cantilever beams

2016

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This work addresses the large amplitude nonlinear vibratory behavior of a rotating cantilever beam, with applications to turbomachinery and turbopropeller blades. The aim of this work is twofold. Firstly, we investigate the effect of rotation speed on the beam nonlinear vibrations and especially on the hardening/softening behavior of its resonances and the appearance of jump phenomena at large amplitude. Secondly, we compare three models to simulate the vibrations. The first two are based on analytical models of the beam, one of them being original. Those two models are discretized on appropriate mode basis and solve by a numerical following path method. The last one is based on a finite-element discretization and integrated in time. The accuracy and the validity range of each model are exhibited and analyzed.

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Section: Introductionmentioning

confidence: 99%

Hardening/softening behavior and reduced order modeling of nonlinear vibrations of rotating cantilever beams

2016

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“…Pour prédire correctement l'évolution des fréquences propres et des modes propres associés en fonction du taux de rotation, les travaux ultérieurs ont intégrés de nombreux paramètres additionnels afin de mieux représenter la géométrie, les effets aérodynamiques ou d'autres contraintes techniques. Ces améliorations permettent de prendre en compte des sections de poutre variables ou non symétriques, un angle de vrillage [109,117], de battement, de traîné ou d'attaque [80,21], un décalage du point d'attache de la poutre avec le centre de rotation [27,79], des inerties de rotation, des masses embarquées [16,70,97] et de nombreuses conditions aux limites [20,126,40]. Au final, tous ces paramètres conduisent à des effets supplémentaires complexes qui ne sont pas pris en compte dans les modèles de poutre classiques.…”

Section: Bibliographieunclassified

Optimization of Shunted Piezoelectric Patches for Vibration Reduction of Complex Structures: Application to a Turbojet Fan Blade

Sénéchal¹,

Thomas²,

Deü³

2010

Volume 5: 22nd International Conference on Design Theory and Methodology; Special Conference on Mechanical Vibration and Noise

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“…Then Eq. [33], [34], [35]). By using the notation from [20] the corresponding Sturm-Liouville problem has the form…”

Section: Eigenoscillations Of Mechanical Systems 523mentioning

confidence: 99%

Eigenoscillations of mechanical systems with boundary conditions containing the frequency

Belinskiy¹,

Dauer²

1998

Quart. Appl. Math.

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Abstract.The problem of eigenoscillations of beam-mass systems is investigated and four examples are developed. For such systems the corresponding Sturm-Liouville problems contain the eigenvalue parameter in the boundary conditions. It is shown that the eigenfunctions for the systems considered form a basis of the appropriate Hilbert space. Rayleigh-Ritz formulas are also developed. Some lower bound estimations for eigenfrequencies are also found. Introduction.As is well known, the set of eigenfunctions of a positive selfadjoint second-order differential operator on L2[0, d] forms a basis of the space involved [1, p. 167]. There exists diverse literature [1] devoted to the problem of determining when a system of eigenfunctions forms a basis for the appropriate Hilbert space. The goal of this work is to contribute to this eigenfunction problem for certain mechanical systems that are defined by a Sturm-Liouville problem with an eigenvalue appearing in the boundary conditions. The intention of this paper is to show how known methods and results from the theory of operators on a Hilbert space can be applied to a class of eigenoscillation

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The transverse vibration of a rotating beam with tip mass: The method of integral equations

Cited by 18 publications

References 6 publications

Hardening/softening behavior and reduced order modeling of nonlinear vibrations of rotating cantilever beams

Hardening/softening behavior and reduced order modeling of nonlinear vibrations of rotating cantilever beams

Optimization of Shunted Piezoelectric Patches for Vibration Reduction of Complex Structures: Application to a Turbojet Fan Blade

Eigenoscillations of mechanical systems with boundary conditions containing the frequency

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