Vibration analysis of rectangular plates coupled with fluid

Institut de Recherche d’Hydro Québec, 1800 Lionel-Boulet Varennes, Quebec, Canada J3X 1S1
Applied Mathematical Modelling (Impact Factor: 2.25). 12/2008; 32(12):2570-2586. DOI: 10.1016/j.apm.2007.09.004


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.
    Full-text · Article · Aug 2015 · Engineering Applications of Computational Fluid Mechanics
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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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    ABSTRACT: The study examined the effect of fluid–structure interaction on global dynamic properties such as vibrational frequency, mode shape, modal curvature, as well as free vibrational responses along E-glass composite, carbon composite, and aluminum beams, respectively. The digital image correlation technique was used to measure the free vibrational responses along the beams in air and water, respectively. The vibration submerged in water exhibited higher frequency modes than the dry vibration under the same excitation. Experimental modal analysis showed that the mode shapes were very close for an aluminum beam with and without the FSI effect while there was a modest difference for a carbon composite beam because the FSI effect is greater for the composite beam. Modal curvatures for the both beams are more influenced by FSI, especially for the composite beam. The curvature is directly related to the bending strain of the beam. This explains why the difference in strains measured for composite structures in air and water, respectively, varies significantly from location to location of the structures under impact loading. One location has much greater difference in strains than another location. The FSI can change potential failure locations of the composite structures because of the change in modal curvatures.
    Full-text · Article · Nov 2013 · Composite Structures
    • "In these methods, the fluid domain or the wet surface is divided into small elements. The fluid finite element method was applied to the hydroelastic vibration analysis of a plate by Chowdhury (1972), Kerboua et al. (2008), Marcus (1978), Muthuveerappan et al. (1979a) (1979b) (1980) and Rao et al. (1993). The boundary integral equation can tackle this problem more easily than the finite element method. "
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    ABSTRACT: The free flexural vibration of a cantilever plate partially submerged in a fluid is investigated. The fluid is assumed to be inviscid and irrotational. The virtual mass matrix is derived by solving the boundary-value problem related to the fluid motion using elliptical coordinates. The introduction of the elliptical coordinates naturally leads to the use of the Mathieu function. Hence, the virtual mass matrix which reflects the effect of the fluid on the natural vibration characteristics is expressed in analytical form in terms of the Mathieu functions. The virtual mass matrix is then combined with the dynamic model of a thin rectangular plate obtained by using the Rayleigh-Ritz method. This combination is used to analyze the natural vibration characteristics of a partially submerged cantilever plate qualitatively. Also, the non-dimensionalized added virtual mass incremental factors for a partially submerged cantilever plate are presented to facilitate the easy estimation of natural frequencies of a partially submerged cantilever plate. It is found that the numerical results are in good agreement with the previous results, thus validating the proposed approach.
    No preview · Article · Jul 2013 · Journal of Fluids and Structures
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