Coupled free vibration analysis of a fluid-filled rectangular container with a sagged bottom membrane

In the present paper, two-dimensional coupled free vibrations of a fluid-filled rectangular container with a sagged bottom membrane are investigated. This system consists of two rigid walls and a membrane anchored along two rigid vertical walls. It is filled with incompressible and inviscid fluid. T...

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Bibliographic Details
Published in:Journal of fluids and structures 2010-02, Vol.26 (2), p.236-252
Main Authors: Daneshmand, F., Ghavanloo, E.
Format: Article
Language:English
Subjects:
Computational fluid dynamics
Containers
Coupled free vibration
Exact sciences and technology
Fluid flow
Fluids
Fluid–membrane system
Fluid–structure interaction
Free vibration
Fundamental areas of phenomenology (including applications)
Mathematical analysis
Membranes
Natural frequency
Physics
Rigid walls
Sagged membrane
Solid mechanics
Structural and continuum mechanics
Vibration, mechanical wave, dynamic stability (aeroelasticity, vibration control...)
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Summary:In the present paper, two-dimensional coupled free vibrations of a fluid-filled rectangular container with a sagged bottom membrane are investigated. This system consists of two rigid walls and a membrane anchored along two rigid vertical walls. It is filled with incompressible and inviscid fluid. The membrane material is assumed to act like an inextensible material with no bending resistance. First, the nonlinear equilibrium equation is solved and the equilibrium shape of the membrane is obtained using an analytical formulation neglecting the membrane weight. The small vibrations about the equilibrium configuration are then investigated. Along the contact surface between the bottom membrane and the fluid, the compatibility requirement is applied for the fluid–structure interactions and the finite element method is used to calculate the natural frequencies and mode shapes of the fluid–membrane system. The vibration analysis of the coupled system is accomplished by using the displacement finite element for the membrane and the pressure fluid-finite element for the fluid domain. The variations of natural frequencies with the pressure head, the membrane length, the membrane weight and the distance between two rigid walls are examined. Moreover, the mode shapes of system are investigated.
ISSN:0889-9746
1095-8622
DOI:10.1016/j.jfluidstructs.2009.11.001