Article

Vibration analysis of rectangular plates coupled with fluid

Mechanical Engineering Department, École de Technologie Supérieure, Canada 1100, Notre Dame Ouest, Montreal, Quebec, Canada H3C 1K3
Applied Mathematical Modelling (Impact Factor: 2.25). 12/2008; 32(12):2570-2586. DOI: 10.1016/j.apm.2007.09.004

ABSTRACT The approach developed in this paper applies to vibration analysis of rectangular plates coupled with fluid. This case is representative of certain key components of complex structures used in industries such as aerospace, nuclear and naval. The plates can be totally submerged in fluid or floating on its free surface. The mathematical model for the structure is developed using a combination of the finite element method and Sanders’ shell theory. The in-plane and out-of-plane displacement components are modelled using bilinear polynomials and exponential functions, respectively. The mass and stiffness matrices are then determined by exact analytical integration. The velocity potential and Bernoulli’s equation are adopted to express the fluid pressure acting on the structure. The product of the pressure expression and the developed structural shape function is integrated over the structure-fluid interface to assess the virtual added mass due to the fluid. Variation of fluid level is considered in the calculation of the natural frequencies. The results are in close agreement with both experimental results and theoretical results using other analytical approaches.

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Available from: Marc Thomas, Aug 12, 2015
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    • "The purpose of this paper is to develop a solidfluid finite element to study the dynamic response of rectangular plate subjected to potential flow. We are expanding the approach used to model rectangular plates and systems of parallel and radial plates submerged in fluid at rest (Kerboua et al., 2007a & 2008) to enable modelling of plates subjected to flowing fluid. This finite element permits us to obtain the low as well as the high frequencies of fluid-structure systems with precision for any combination of boundary conditions without changing the displacement field. "
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    ABSTRACT: Elastic structures subjected to fluid flow undergo a considerable change in their dynamic behaviour and can lose their stability. In this article we describe the development of a fluid-solid finite element to model plates subjected to flowing fluid under various boundary conditions. The mathematical model for the structure is developed using a combination of the hybrid finite element method and Sanders' shell theory. The membrane displacement field is approximated by bilinear polynomials and the transversal displacement by an exponential function. Fluid pressure is expressed by inertial, Coriolis and centrifugal fluid forces, written respectively as function of acceleration, velocity and transversal displacement. Bernoulli's equation for the fluid-solid interface and partial differential equation of potential flow are applied to calculate the fluid pressure. An impermeability condition ensures contact between the system of plates and the fluid. Mass and rigidity matrices for each element are calculated by exact integration. Calculated results are in reasonable agreement with other analytical theories.
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    • "Analytical approaches to determine the natural frequencies with the added mass effect were based on the assumption that the mode shapes do not change with FSI while the frequencies change [3] [4] [5] [6]. Because FSI is a complex problem, many numerical techniques have been developed by coupling one solver for structures to another solver for fluid media [7] [8] [9] [10] [11] [12]. "
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    Composite Structures 11/2013; 105:269–278. DOI:10.1016/j.compstruct.2013.05.032 · 3.32 Impact Factor
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    • "In this paper we base our theory on a developed method for analysis of a thin plate in a vacuum and in inviscid incompressible stationary fluid [23] [24]. "
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    ABSTRACT: A method capable of predicting the root mean square displacement response of a thin structure subjected to a turbulent boundary-layer-induced random pressure field is presented. The basic formulation of the dynamic problem is an efficient approach combining classic thin shell theory and the finite element method, in which the finite elements are flat rectangular elements with six degrees of freedom per node. The displacement functions are derived from thin shell theory. Description of the turbulent pressure field is based on the Corcos formulation for cross spectral density of pressure fluctuations. A numerical approach is proposed to obtain the total root mean square displacements of the structure. Exact integration over surface and frequency leads to an expression for the response in terms of the characteristics of the structure and flow. An in-house program based on the presented method was developed. The total root mean square displacements of a thin plate under different boundary conditions subjected to a turbulent boundary layer were calculated and illustrated as a function of free stream velocity and damping ratio and the effects of flow direction on the response were also investigated. In addition, the power spectral densities of the displacements of an SFSF plate subjected to a fully developed turbulent flow were studied. The total root mean square radial displacement of a thin cylindrical shell was obtained and compared favorably with that in the literature.
    Journal of Sound and Vibration 11/2009; 328(1):109-128. DOI:10.1016/j.jsv.2009.07.027 · 1.86 Impact Factor
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