VIBRATIONS OF FLUID-FILLED HERMETIC CANS

doi:10.1006/jfls.1999.0267

Journal of Fluids and Structures

Volume 14, Issue 2, February 2000, Pages 235-255

https://doi.org/10.1006/jfls.1999.0267 Get rights and content

Abstract

Free, conservative vibrations of a hermetic can, simply supported at the base, are studied. The can is composed by a circular cylindrical shell and two identical circular plates connected to the shell at its ends. The artificial spring method, which is an extension of the classical Rayleigh–Ritz method, is used to solve the system by using substructuring. The can is studied empty and filled with an inviscid and incompressible fluid. Fluid volume conservation is applied. The interaction between the plates and the shell via the fluid is considered, and exact expressions for the fluid velocity potential are used. The effect of flexibility of joints between plates and shell is investigated. Results for a fluid-filled, simply supported shell closed by rigid ends are also obtained and compared to the classical open-end shell.

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Cited by (14)

Vibration analysis of a system of partially-filled interconnected cylindrical shells representing a fast reactor
2022, Journal of Fluids and Structures
Citation Excerpt :
More complex fluid–shell systems have also been studied in the past. These include a fully-filled cylindrical shell partially immersed in dense fluid (Amabili, 1999), a system of partially-filled cylindrical shell with two circular plates attached at both ends (Amabili, 2000b), partially-filled cylindrical tank supported at the top (Yu and Whittaker, 2020), a system of a rigid solid cylinder submerged in fluid contained inside a concentric rigid cylinder (Fritz, 1972), a system of two concentric cylinders with fluid present through the height of the cylinders (Chen and Rosenberg, 1975; Yu and Whittaker, 2021), a system of two completely-filled concentric cylinders with the inner cylinder suspended from the top of the outer cylinder (Au-Yang, 1976), a cylinder with one or more smaller cylinder(s) placed inside eccentrically (Chung and Chen, 1977; Jeong et al., 2001), and a partially-filled cylinder supported at the bottom with a concentrically placed inverted cylinder supported at the top (Askari and Daneshmand, 2009; Askari et al., 2011; Moshkelgosha et al., 2017). The dynamic behavior of such systems has been found to depend on number, dimensions and location of cylinders, height of fluid, and support conditions.
Dynamics of a system comprising three interconnected partially-filled concentric cylindrical shells is studied. The outermost shell is upright, and is head-supported. The base of the inner shell is attached to that of the outermost shell. The innermost shell is inverted, and is supported through roof. This shell is partially submerged. Height of fluid in all upright shells is same. This system can be considered to represent a fast breeder reactor. Suitable functional forms are considered to describe the fluid’s velocity potential, which leads to the dynamic properties through an energy-based approach. Appropriate changes in the parameters of the solution are shown to produce results for multiple fluid–shell systems studied in the past. A parametric study shows that the natural frequencies of the system are most affected by the fluid height. A smaller annular gap between outer vessels led to lower bulging, but greater sloshing frequencies. Influence of the innermost shell on these results was small. The analytical formulation and the results presented in the paper can be used for validation in future studies on a range of fluid–shell systems.
Vibro-acoustic analysis of combined elliptical–cylindrical–elliptical shells immersed in acoustic medium
2021, Journal of Fluids and Structures
Citation Excerpt :
However, it should not be denied that more and more scholars have paid attention to the vibration and acoustics of combined shell structure. Amabili (1997b, 2018, 2000) studied the vibrations of cylindrical shell-plate structures partially filled with liquids, which can be regarded as a finite-fluid-medium problem, and the effects of the liquid level on the vibrations are studied. Qu et al. (2015) and Qu and Meng (2016) predicted vibration and acoustic responses of submerged coupled spherical–cylindrical–spherical shells by a semi-analytical method, where the structure was stiffened by circumferential rings and longitudinal stringers.
The vibro-acoustic behaviors of combined elliptical–cylindrical–elliptical shells (CECES) is studied by the spectral-energy boundary element approach. The Jacobian orthogonal polynomials and the variational principles are employed to establish the dynamic model of the CECES. The Kirchhoff–Helmholtz integral equation is used to calculate the exterior sound radiation of the CECES. The Chebyshev polynomials and the Fourier series are adopted to express the acoustic variables along the meridional direction and the circumferential direction of the CECES, respectively. In this case, the two-dimensional Helmholtz integral formulation is simplified to a one-dimensional problem. By using the spectral boundary element and Chebyshev collocation points to discretize the acoustic boundary, the mathematical difficulties of traditional boundary element method which needs physical points to integrate can be overcome. Furthermore, to solve the problem of singularity and frequency non-uniqueness in the acoustic solution, the CHIEF method is used. The full vibro-acoustic coupling model is established by considering the work due to the external field acting on the CECES surface. By comparing to the acoustic responses obtained by the coupled BEM/FEM, the present method is proved to have enough accuracy for predicting the vibro-acoustic behaviors of CECES. Furthermore, study on the influence of the circumferential wave modes, boundary condition and acoustic medium on vibro-acoustic behaviors of the CECES is made by several numerical examples, which contributes to the preliminary design of the CECES.
Free vibration of multiple rectangular plates coupled with a liquid
2013, International Journal of Mechanical Sciences
Fuel assemblies of a research reactor consist of a number of rectangular fuel plates with an equal gap and the coolant flows between the fuel plates for heat exchange. The paper deals with a theoretical dynamic model of the fuel assembly submerged in the coolant, and presents a free vibration analysis of a bundle of identical rectangular plates fully in contact with an ideal liquid. The orthogonal polynomial functions, as admissible functions, were generated using the Gram–Schmidt process to approximate the wet dynamic displacements of the plates with a clamped-clamped-free-free boundary condition. The liquid displacement potential satisfying the boundary conditions was derived, and the wet dynamic modal functions of the plates were expanded by the finite Fourier transform for a compatibility requirement along the contacting surface between the plates and the liquid. The natural frequencies under the wet condition were calculated using the Rayleigh–Ritz method based on minimizing the Rayleigh quotient of the ratio between the maximum potential energy and total kinetic energy. The comparison showed excellent agreement between the results from the proposed theoretical method with the finite element analysis results. The effect of the liquid gap between the plates on the normalized natural frequencies was discussed.
Coupled vibration of a partially fluid-filled cylindrical container with a cylindrical internal body
2009, Journal of Fluids and Structures
In the present paper a method is proposed to investigate the effects of a rigid internal body on the coupled vibration of a partially fluid-filled cylindrical container. The internal body is a thin-walled and open-ended cylindrical shell. The internal body is concentrically and partially submerged inside a container. The radial and axial distances between the internal body and the container are filled with fluid. Along the contact surface between the container and the fluid, the compatibility requirement for the fluid–structure interactions is applied and the Rayleigh–Ritz method is used to calculate the natural frequencies and modes of a partially fluid-filled cylindrical container. The fluid domain is continuous, simply connected, and non-convex. The fluid is assumed to be incompressible and inviscid. The velocity potential for fluid motion is formulated in terms of eigenfunction expansions for two distinct fluid regions. The resulting equations are solved by using the Galerkin method. The results from the proposed method are in good agreement with experimental and numerical solutions available in the literature for the partially water-filled cylindrical container without internal body. A finite element analysis is also used to check the validity of the present method for the partially water-filled cylindrical container with internal body. The effects of the fluid level, internal body radius, and internal body length on the natural frequencies of the coupled system are also investigated.
Hydroelastic vibration of two annular plates coupled with a bounded compressible fluid
2006, Journal of Fluids and Structures
A theoretical study on a linear hydroelastic vibration of two annular plates coupled with a bounded fluid is presented. The proposed method, based on the Rayleigh–Ritz method and the finite Hankel transform, is verified through a finite element analysis by using a commercial computer code, with an excellent accuracy. It is assumed that plates with an unequal thickness and with an unequal inner radius are clamped along their edges and an inviscid compressible fluid fills the space between the annular plates and the outer rigid vessel. When the two annular plates are identical, distinct in-phase and out-of-phase modes are observed. By increasing the difference in the plate thickness, the symmetric in-phase and out-of-phase modes with respect to the middle plane of the system are gradually shifted to pseudo in-phase and out-of-phase modes, and eventually they are changed to mixed modes. It is found that the natural frequencies decrease with an increase of the fluid compressibility, and additional modes due to a fluid concentration are observed when the plates are coupled with a compressible fluid. The fluid compressibility effect on the natural frequency is dominant in the out-of-phase modes and the higher modes. Also, the effects of the fluid thickness or the distance between the plates and the inner radius of the plates on the natural frequencies of the wet modes are investigated.
Hydroelastic analysis of fluid storage tanks by using a boundary integral equation method
2004, Journal of Sound and Vibration
Citation Excerpt :
For the symmetric and anti-symmetric mode shapes (i=0,j=0), the finite element predictions are, respectively, 11.2% and 23.7% higher than those analytically calculated by Huang and Soedel [24], in which similar discrepancies were observed between their predictions based on the receptance method and finite element calculations. On the other hand, the predicted wet frequencies in Table 10 show a maximum difference of 5.1% in comparison with the analytical calculations of Amabili [23], except for the anti-symmetric mode shape (i=0,j=0). It should also be noted that there is no results presented for the plate-dominant symmetric modes (i=0,j=0) and (i=0,j=1) in Table 10.
This paper presents a boundary integral equation method in conjunction with the method of images, in order to investigate the dynamic behaviour (wet frequencies and associated mode shapes) of fluid containing structures. In the analysis of the linear fluid–structure system, it is assumed that the fluid is ideal, and fluid forces are associated with inertial effects of the contained fluid. This implies that the fluid pressure on the wetted surface of the structure is in phase with the structural acceleration. The in vacuo dynamic properties of the dry structure are obtained by using standard finite element software. In the wet part of the analysis, the fluid–structure interaction effects are calculated in terms of the generalized added mass coefficients by use of the boundary integral equation method together with the method of images in order to impose the Φ=0 boundary condition on the free surface. In this study, three different test cases are considered: (i) a clamped–free cylindrical tank with a rigid bottom; (ii) a flexible circular plate in a rigid cylindrical tank and (iii) a flexible cylindrical shell with flexible end plates (hermetic can). The fluid storage tanks in this investigation are assumed partially or completely filled with water. To assess the influence of the contained fluid on the dynamic characteristics, the wet natural frequencies and associated mode shapes are calculated. The predictions compare well with available experimental and numerical data.

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Regular ArticleVIBRATIONS OF FLUID-FILLED HERMETIC CANS

Abstract

Journal of Sound and Vibration

Journal of Fluids and Structures

Journal of Fluids and Structures

Journal of Sound and Vibration

Journal of Sound and Vibration

Journal of Sound and Vibration

Journal of Sound and Vibration

Journal of Fluids and Structures

Journal of Sound and Vibration

Journal of Sound and Vibration

Journal of Sound and Vibration

Journal of Sound and Vibration

Journal of Sound and Vibration

Journal of Sound and Vibration

Journal of Sound and Vibration

Regular Article
VIBRATIONS OF FLUID-FILLED HERMETIC CANS