A displacement method for the analysis of vibrations of coupled fluid-structure systems (original) (raw)
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International Journal for Numerical Methods in Engineering, 1979
The finite element method is used for the computation of the variational modes of the system composed of an elastic tank partially filled with a compressible liquid. We propose, on the one hand, a direct approach based on a three field mixed variational formulation, and, on the other hand, a variational modal interaction scheme allowing the use of the acoustic eigenmodes of the liquid in a rigid motionless enclosure and the hydroelastic modes of the enclosure. Numerical results show the advantage of the second procedure.
Efficient solution of fluid-structure vibration problems
Applied Numerical Mathematics, 2001
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.
International Journal for Numerical Methods in Engineering, 1986
We present a new finite element analysis of the linear dynamic responses of a slender fluid-. structure system, namely the elasto-acoustic beam, neglecting flow and viscosity effects. Using one unknown field in the fluid, namely the 'mass-flow' corresponding to a cross-section mean value of the longitudinal displacement field component, an original symmetric formulation is derived which does not exhibit the usual spurious modes associated with the irrotationality constraint occurring in displacements formulations of fluid-structure problems.
Finite element analysis of compressible and incompressible fluid-solid systems
Mathematics of Computation, 1998
This paper deals with a finite element method to solve interior fluid-structure vibration problems valid for compressible and incompressible fluids. It is based on a displacement formulation for both the fluid and the solid. The pressure of the fluid is also used as a variable for the theoretical analysis yielding a well posed mixed linear eigenvalue problem. Lowest order triangular Raviart-Thomas elements are used for the fluid and classical piecewise linear elements for the solid. Transmission conditions at the fluid-solid interface are taken into account in a weak sense yielding a nonconforming discretization. The method does not present spurious or circulation modes for nonzero frequencies. Convergence is proved and error estimates independent of the acoustic speed are given. For incompressible fluids, a convenient equivalent stream function formulation and a post-process to compute the pressure are introduced.
Nuclear Engineering and Design, 1983
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.
Numerical investigation of structural behavior during fluid excited vibrations
Revue européenne de mécanique numérique, 2007
In the present paper different occurring phenomena during the interaction between certain structural configurations and laminar incompressible flows are investigated. Preliminary investigations concerning the grid movement technique provide the basis for the adequate treatment of the fluid structure interaction problems. Several mechanisms according to real experiments are presented. Systematical numerical studies of material parameters are performed on the basis of a moderately complex fluid structure interaction test configuration. The solution procedure involves the finite-volume flow solver FASTEST, the finite-element structural solver FEAP, and the coupling interface MpCCI. RÉSUMÉ. Dans cet article des phénomènes différents apparaissant pendant l'interaction entre certaines configurations structurales et des écoulements laminaires et incompressibles sont explorés. Des investigations précédentes concernant la technique de mouvement du maillage fournissent la base pour le traitement adéquat des problèmes d'interaction fluide structure. Conformément aux expériences réelles divers mécanismes sont représentés. A la base des configurations d'interaction fluide structure de test faiblement complexe des études numériques des paramètres matériaux sont effectuées systématiquement. La procédure de résolution inclut le solveur d'écoulement du fluide basé sur la méthode des volumes finis FASTEST, le solveur structural basé sur la méthode des éléments finis FEAP et l'interface de couplage MpCCI.
Finite element computation of the vibrations of a plate-fluid system with interface damping
Computer Methods in Applied Mechanics and Engineering, 2001
This paper deals with a finite element method to compute the vibrations of a coupled fluid-solid system subject to an external harmonic excitation. The system consists of an acoustic fluid and a plate, with a thin layer of a noise damping viscoelastic material separating both media. The fluid is described by displacement variables whereas the plate is modeled by Reissner-Mindlin equations. Face elements are used for the fluid and MITC3 elements for the bending of the plate. The effect of the damping material is taken into account by adequately relaxing the kinematic constraint on the fluid-solid interface. The non-linear eigenvalue problem arising from the free vibrations of the damped coupled system is also considered. The dispersion equation is deduced for the simpler case of a fluid in a hexahedral rigid cavity with an absorbing wall. This allows computing analytically its eigenvalues and eigenmodes and comparing them with the finite element solution. The numerical results show that the coupled finite element method neither produce spurious modes nor locks when the thickness of the plate becomes small. Finally the computed resonance frequencies are compared with those of the undamped problem and with the complex eigenvalues of the above non-linear spectral problem.