Vibration analysis of rotating 3D beams by the p-version finite element method

Stoykov, Stanislav; Ribeiro, Pedro

doi:10.1016/j.finel.2012.10.008

Cited by 40 publications

(35 citation statements)

References 26 publications

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“…For the VK model, taken from earlier studies of the literature [2,4,37,58,65], it has been found that it completely fails to represent accurately (even qualitatively) the nonlinear oscillations of the beam, mainly because the physical source of the nonlinearities is missing. An original analytical model, the Inxt.…”

Section: Resultsmentioning

confidence: 99%

“…This is the model considered in [2,4,37,58,65]. To solve this problem, one has to choose two principal unknowns, for the transverse and axial motion.…”

Section: Equations Of Motionmentioning

confidence: 99%

“…Then, the framework of nonlinear modes and invariant manifolds was applied to a simplified model of a rotating beam based on a von Kármán formulation [2,37,58], where the goal was the size reduction in the model and its accuracy as compared to a full-scale model. A von Kármán model was also used in [65] with a p-version finite-element method, whereas more refined finite-element models, with several levels of simplifications, were proposed and compared in [70]. In both cases, time simulations are shown.…”

Section: Introductionmentioning

confidence: 99%

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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: Resultsmentioning

confidence: 99%

“…This is the model considered in [2,4,37,58,65]. To solve this problem, one has to choose two principal unknowns, for the transverse and axial motion.…”

Section: Equations Of Motionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

2016

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“…Moreover, authors concluded that additional shear stresses which appeared while bending and torsion were coupled have an essential influence on the beam's dynamics. In the latest paper [31] the p-version of finite element was used for 3D Timoshenko beam model in which two types of nonlinearity were considered, a nonlinear strain-displacement relation and inertia forces due to rotation. The deformation in a longitudinal direction due to warping was taken into account.…”

Section: Introductionmentioning

confidence: 99%

Equations of motion of rotating composite beam with a nonconstant rotation speed and an arbitrary preset angle

2014

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In the presented paper the equations of motion of a rotating composite Timoshenko beam are derived by utilising the Hamilton principle. The nonclassical effects like material anisotropy, transverse shear and both primary and secondary cross-section warpings are taken into account in the analysis. As an extension of the other papers known to the authors a nonconstant rotating speed and an arbitrary beam's preset (pitch) angle are considered. It is shown that the resulting general equations of motion are coupled together and form a nonlinear system of PDEs. Two cases of an open and closed box-beam cross-section made of symmetric laminate are analysed in details. It is shown that considering different pitch angles there is a strong effect in coupling of flapwise bending with chordwise bending motions due to a centrifugal force. Moreover, a consequence of terms related to nonconstant rotating speed is presented. Therefore it is shown that both the variable rotating speed and nonzero pitch angle have significant impact on systems dynamics and need to be considered in modelling of rotating beams.

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“…A setting angle and a rigid hub are included in the model. The equation of motion is derived in the rotating coordinate system, and the rotation is taken into account by the inertia forces [10]. The beam may vibrate in space, i.e.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear Vibrations of Rotating 3d Tapered Beams With Arbitrary Cross Sections

Stoykov¹,

Margenov²

2014

Proceedings of the 4th International Conference on Computational Methods in Structural Dynamics and Earthquake Engineering (COM

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Abstract. The geometrically nonlinear vibrations of 3D beams that rotate about a fixed axis are investigated by the p-version finite element method. The beams are considered to be tapered, i.e. with variable thickness along its length, and with arbitrary cross sections. The beam model is based on INTRODUCTIONRotating beams are used to model and investigate the dynamics of helicopter blades, jet engine turbine blades, robot arms, wind turbine blades, etc. Many studies have been performed for modeling rotating beams about a fixed axis. The linear natural frequencies of beams that rotate with constant speed were investigated by many researchers, for example in [1][2][3][4][5]. Works that consider geometrically nonlinear models of rotating beams may be found, for example [6][7][8]. In what concerns modern wind turbine blades, most of them are constructed with load carrying box girder inside the blade and shells on the surface of the blade [9]. The purpose of the box girder is to make the blade stronger and stiffer while the shells around the box girder form the aerodynamic shape. Thus, the dynamic behavior of the wind turbine blade might be determined mainly from the load carrying box, even though the shells contribute small bending strength.In the current work, a model of beams rotating about a fixed axis with constant speed of rotation is presented. A setting angle and a rigid hub are included in the model. The equation of motion is derived in the rotating coordinate system, and the rotation is taken into account by the inertia forces [10]. The beam may vibrate in space, i.e. it may perform longitudinal, torsional and bending deformations, the model is based on Timoshenko's theory for bending and assumes that under torsion, the cross section deforms only in longitudinal direction due to warping [11]. Geometrical type of nonlinearity is considered and the equation of motion is derived by the principle of virtual work.Thin-walled box beams with linearly varying thickness and width are investigated. First, the derived model is validated by generating a fine mesh of three-dimensional finite elements. Then, the influence of the setting angle and the speed of rotation on the natural frequencies is examined. Forced vibrations of rotating beams due to harmonic forces are presented.

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Vibration analysis of rotating 3D beams by the p-version finite element method

Cited by 40 publications

References 26 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

Equations of motion of rotating composite beam with a nonconstant rotation speed and an arbitrary preset angle

Nonlinear Vibrations of Rotating 3d Tapered Beams With Arbitrary Cross Sections

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