Fluid-Structure Finite Element Vibrational Analysis

Kiefling, L.; Feng, G. C.

doi:10.2514/3.61357

Cited by 89 publications

(57 citation statements)

References 2 publications

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“…Let us remark that such a spectral pollution appears in standard finite element discretizations of other formulations of this same problem (see [22,8]). …”

Section: Spectral Approximationmentioning

confidence: 96%

“…In early works [25], the acoustic wave equation is written in terms of the pressure, which leads to non-symmetric eigenvalue problems (see also [6]). Alternatively, the fluid can be modeled by using the displacement [22,4,8,3], a displacement potential on its own [7,24] or combined with the pressure [10]. We refer to [7] for a comparison of these different formulations.…”

Section: Introductionmentioning

confidence: 99%

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Finite element analysis for a pressure–stress formulation of a fluid–structure interaction spectral problem

Meddahi

Mora

Rodrı́guez

2014

Computers & Mathematics with Applications

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Abstract. The aim of this paper is to analyze an elastoacoustic vibration problem employing a dual-mixed formulation in the solid domain. The Cauchy stress tensor and the rotation are the primary variables in the elastic structure while the standard pressure formulation is considered in the acoustic fluid. The resulting mixed eigenvalue problem is approximated by a conforming Galerkin scheme based on the lowest order Lagrange and Arnold-Falk-Winther finite element subspaces in the fluid and solid domains, respectively. We show that the scheme provides a correct approximation of the spectrum and prove quasioptimal error estimates. Finally, we report some numerical experiments.

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“…Let us remark that such a spectral pollution appears in standard finite element discretizations of other formulations of this same problem (see [22,8]). …”

Section: Spectral Approximationmentioning

confidence: 96%

Section: Introductionmentioning

confidence: 99%

Finite element analysis for a pressure–stress formulation of a fluid–structure interaction spectral problem

Meddahi

Mora

Rodrı́guez

2014

Computers & Mathematics with Applications

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“…As earlier noted by Kiefling and Feng [23], Akkas, Akay, and Yilmaz [24], and Hamdi, Ousset, and Verchery [25], the displacement-based fluid elements employed in practice can exhibit spurious oscillations. We address this specific problem in this paper.…”

Section: Introductionmentioning

confidence: 92%

“…Note that these modes do not represent surface waves, since gravity and sloshing were not included in the formulation. These displacement patterns represent unphysical (spurious) modes which occur at non-zero frequencies [23][24][25].…”

Section: Tall Water Columnmentioning

confidence: 99%

A study of displacement-based fluid finite elements for calculating frequencies of fluid and fluid-structure systems

Olson

Bathe

1983

Nuclear Engineering and Design

141

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The widely-used displacement-based finite element formulation for inviscid, compressible, small displacement fluid motions is examined, with the specific objective of calculating fluid-structure frequencies. It is shown that the formulation can be employed with confidence to predict the static response of fluids. Also the resonant frequencies of fluids in rigid cavities and the frequencies of fluids in flexible boundaries are solved successfully if a penalty on rotations is included in the formulation. However, the reason for writing this paper is that problems involving structures moving through fluids that behave almost incompressibly -such as an ellipse vibrating on a spring in water -could not be solved satisfactorily, for which a general explanation is given.

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“…To avoid this drawback, different variables have been proposed to describe the fluid: Everstine [6] used the velocity potential obtaining a symmetric but quadratic eigenvalue problem; Kiefling and Feng [7] considered displacement variables, but they show that spurious modes arise when standard finite elements are used. More recently, alternative discretizations avoiding these spurious modes have been proposed by Chen and Taylor [4] and Bermúdez and Rodríguez [2].…”

Section: Introductionmentioning

confidence: 99%

Efficient solution of fluid-structure vibration problems

Mellado

Rodrı́guez

2001

Applied Numerical Mathematics

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This paper deals with the numerical computation of elastoacoustic vibration modes. We consider a redundant description of the fluid by means of pressure and displacement potential variables introduced by Morand and Ohayon. We analize a finite element discretization leading to a well posed symmetric banded eigenvalue problem. An iterative algorithm requiring to solve sparse linear systems with one degree of freedom per fluid node is obtained. We show that, for acoustic modes, this method coincides with a consistent discretization of the standard potential formulation. Numerical experiments are included to validate the proposed methodology for elastoacoustic vibrations.

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Fluid-Structure Finite Element Vibrational Analysis

Cited by 89 publications

References 2 publications

Finite element analysis for a pressure–stress formulation of a fluid–structure interaction spectral problem

Finite element analysis for a pressure–stress formulation of a fluid–structure interaction spectral problem

A study of displacement-based fluid finite elements for calculating frequencies of fluid and fluid-structure systems

Efficient solution of fluid-structure vibration problems

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