Effect of the centrifugal forces on the finite element eigenvalue solution of a rotating blade: a comparative study

Maqueda, Luis G.; Bauchau, Olivier A.; Shabana, Ahmed A.

doi:10.1007/s11044-007-9070-6

Cited by 25 publications

(16 citation statements)

References 16 publications

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“…As pointed out in [16], the form of the mass matrix of 3D solid finite elements does not change under orthogonal coordinate transformation, i.e. P T MP = M. The cost of FE reevaluation of the nodal centrifugal force for each misalignment scenario can be avoided by employing the lumped mass formulation, i.e.…”

Section: Modeling Of Disk Misalignmentmentioning

confidence: 99%

Parameterized reduced order modeling of misaligned stacked disks rotor assemblies

Ganine¹,

Laxalde²,

Michalska³

et al. 2011

Journal of Sound and Vibration

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Light and flexible rotating parts of modern turbine engines operating at supercritical speeds necessitate application of more accurate but rather computationally expensive 3D FE modeling techniques. Stacked disks misalignment due to manufacturing variability in the geometry of individual components constitutes a particularly important aspect to be included in the analysis because of its impact on system dynamics. A new parametric model order reduction algorithm is presented to achieve this goal at affordable computational costs. It is shown that the disks misalignment leads to significant changes in nominal system properties that manifest themselves as additional blocks coupling neighboring spatial harmonics in Fourier space. Consequently, the misalignment effects can no longer be accurately modeled as equivalent forces applied to a nominal unperturbed system. The fact that the mode shapes become heavily distorted by extra harmonic content renders the nominal modal projection based methods inaccurate and thus numerically ineffective in the context of repeated analysis of multiple misalignment realizations. The significant numerical bottleneck is removed by employing an orthogonal projection onto the subspace spanned by first few Fourier harmonic basis vectors. The projected highly sparse systems are shown to accurately approximate the specific misalignment effects, to be inexpensive to solve using direct sparse methods and easy to parameterize with a small set of measurable eccentricity and tilt angle parameters. Selected numerical examples on an industrial scale model are presented to illustrate the accuracy and efficiency of the algorithm implementation.

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Section: Modeling Of Disk Misalignmentmentioning

confidence: 99%

Parameterized reduced order modeling of misaligned stacked disks rotor assemblies

Ganine¹,

Laxalde²,

Michalska³

et al. 2011

Journal of Sound and Vibration

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“…The bending, extensional, and shear energies are considered here, which are denoted as U b , U e , and U s , respectively. For simplicity, bending is restricted to occur in the x y plane and the energy terms are [17]:…”

Section: ∂R/∂z)]/2 and 23 = [(∂R/∂ Y) T (∂R/∂z)]/2mentioning

confidence: 99%

“…The nondimensional shear factor for a bending structure with a rectangular cross section is k y = 10(1 + ν)/(12 + 11ν) [17], where ν denotes Poisson's ratio. The normal strain vector , reduced matrix of elastic coefficients E, and curvature in the x y plane κ z are defined as:…”

Section: ∂R/∂z)]/2 and 23 = [(∂R/∂ Y) T (∂R/∂z)]/2mentioning

confidence: 99%

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The finite element absolute nodal coordinate formulation incorporated with surface stress effect to model elastic bending nanowires in large deformation

Lilley

2009

Comput Mech

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Surface stress was incorporated into the finite element absolute nodal coordinate formulation in order to model elastic bending of nanowires in large deformation. The absolute nodal coordinate formulation is a numerical method to model bending structures in large deformation. The generalized Young-Laplace equation was employed to model the surface stress effect on bending nanowires. Effects from surface stress and large deformation on static bending nanowires are presented and discussed. The results calculated with the absolute nodal coordinate formulation incorporated with surface stress show that the surface stress effect makes the bending nanowires behave like softer or stiffer materials depending on the boundary condition. The surface stress effect diminishes as the dimensions of the bending structures increase beyond the nanoscale. The developed algorithm is consistent with the classical absolute nodal coordinate formulation at the macroscale.

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“…These solutions help understanding the behavior of the substructured models, the nature of the critical velocity and the tendency of this velocity to increase as the number of substructures is increased as well. A geometrically exact beam model has also been compared to four different nonlinear elastic ANCF models by Maqueda et al [9]. In their work, the effect of the centrifugal forces on the flap and lag modes of a rotor blade was studied.…”

Section: Introductionmentioning

confidence: 99%

Stability analysis of a substructured model of the rotating beam

Valverde

García-Vallejo

2008

Nonlinear Dyn

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One of the most well-known situations in which nonlinear effects must be taken into account to obtain realistic results is the rotating beam problem. This problem has been extensively studied in the literature and has even become a benchmark problem for the validation of nonlinear formulations. Among other approaches, the substructuring technique was proven to be a valid strategy to account for this problem. Later, the similarities between the absolute nodal coordinate formulation and the substructuring technique were demonstrated. At the same time, it was found the existence of a critical angular velocity, beyond which the system becomes unstable that was dependent on the number of substructures. Since the dependence of the critical velocity was not so far clear, this paper tries to shed some light on it. Moreover, previous studies were focused on a constant angular velocity analysis where the effects of Coriolis forces were neglected. In this paper, the influence of the Coriolis force term is not neglected. The influence of the reference condi-J. Valverde ( )

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Effect of the centrifugal forces on the finite element eigenvalue solution of a rotating blade: a comparative study

Cited by 25 publications

References 16 publications

Parameterized reduced order modeling of misaligned stacked disks rotor assemblies

Parameterized reduced order modeling of misaligned stacked disks rotor assemblies

The finite element absolute nodal coordinate formulation incorporated with surface stress effect to model elastic bending nanowires in large deformation

Stability analysis of a substructured model of the rotating beam

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