Dynamic Analysis of Rotating Curved Beam With a Tip Mass

Park, J.-H.; Kim, J.-H.

doi:10.1006/jsvi.1999.2457

Cited by 24 publications

(14 citation statements)

References 20 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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“…Generally speaking, curved beams (arches) have, based on curvature, been classified as [19]: shallow arch (subtended angle < 40 • ) and deep arch (40 • < subtended angle < 180 • ). All the results below are obtained by nonlinear formulation.…”

Section: Effect Of the Shallowness Of The Curved Beammentioning

confidence: 99%

“…It was indicated that the curved beam with moderate curvature is important for understanding the characteristic of the curved structures, however, in Ref. [19], the radius of the curvature of the curved beam is so large that the curved beam approaches a straight beam, therefore the finite element method used in this paper is not persuasive enough. Since Lagrange element formulation is much less susceptible to shear locking than the serendipity formulation, and the completely integrated cubic Lagrange element exhibits no locking, no spurious eigenvalues and rapid convergence to thin plated solution [20], one dimensional cubic Lagrange element is developed to discrete the curved beam by isoparametric formulation in this paper.…”

Section: Introductionmentioning

confidence: 96%

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Geometric nonlinear dynamic analysis of curved beams using curved beam element

Pan

Liu

2011

Acta Mech Sin

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Instead of using the previous straight beam element to approximate the curved beam, in this paper, a curvilinear coordinate is employed to describe the deformations, and a new curved beam element is proposed to model the curved beam. Based on exact nonlinear strain-displacement relation, virtual work principle is used to derive dynamic equations for a rotating curved beam, with the effects of axial extensibility, shear deformation and rotary inertia taken into account. The constant matrices are solved numerically utilizing the Gauss quadrature integration method. Newmark and Newton-Raphson iteration methods are adopted to solve the differential equations of the rigid-flexible coupling system. The present results are compared with those obtained by commercial programs to validate the present finite method. In order to further illustrate the convergence and efficiency characteristics of the present modeling and computation formulation, comparison of the results of the present formulation with those of the ADAMS software are made. Furthermore, the present results obtained from linear formulation are compared with those from nonlinear formulation, and the special dynamic characteristics of the curved beam are concluded by comparison with those of the straight beam.

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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.…”

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