Liquid vibrations in a container with a membrane at the free surface (original) (raw)
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Acoustic Influence on the Vibration of a Cylindrical Membrane Drum Filled with a Compressible Fluid
International Journal of Applied Mechanics
The study of the dynamic behavior of a membrane in contact with a fluid is interesting due to the numerous applications in technology. The vibro-acoustic behavior of a circular membrane in a cylindrical container or a membrane drum filled with a nonviscous fluid is analyzed. A boundary element method is used and the acoustic pressure over the boundary is calculated employing the Kirchhoff’s integral equation and that with the equation of motion of the membrane, the natural frequencies of vibration are obtained. Furthermore, the effect of the drum height, drum radius, membrane material density, tension parameter and fluid density on the frequencies are evaluated, as well as the variation of the fluid mass coefficient with the wave number. Validation of the method is made comparing the results with those obtained by other authors and theories.
Vibration analysis of fluid-filled rubberlike membrane structure. II
39th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference and Exhibit, 1998
The interaction problem of highly flexible membrane and fluid are very important in various industries. In this paper we consider the two dimensional rectangular tank filled with a fluid of which surface is covered by a rubber membrane, and investigate its behavior in order to estimate the interaction behavior. The membrane is assumed to be the Ogden's rubberlike membrane which includes material and geometrical nonlinearities. The fluid is water and assumed to be potential flow. We consider the time historical response subjected to horizontal sinusoidal acceleration which is important to the most of practical usage. The arbitrary Lagrangian-Eulerian finite element method is employed to take account of the moving boundary of the fluid Behavior such as deformed membrane profile, stress distribution, manner of flow and so on are calculatedin the vicinity of natural frequency and discussed. In these numerical examples, the similar behavior to liquid sloshing is observed except for in the neighborhood of the interface, although there is no free surface because of the existence of the membrane cover. Thus it is found that the "Graduate Student. Member AIAA * 'Associate Professor. Department of Aerospace Engineering. Member AIAA Copyright© 1997 by the American Institute of Aeronautics and Astronautics, Inc. AH rights reserved. hydroelastic system composed of the highly flexible membrane coupled with the fluid, is strongly affected by fluid's own motion such as the well-known nonlinearities related to the motion of fluid's free surface.
Sloshing in a vertical circular cylindrical container with a vertical baffle
American Society of Mechanical Engineers, Fluids Engineering Division (Publication) FEDSM, 2010
The linear problem of liquid sloshing in a cylindrical container with a vertical baffle is considered in the present paper. In this study, a theoretical oriented approach is developed for calculating the natural frequencies of liquid. The baffle is a thin-walled and open-ended cylindrical shell that is concentrically placed and partially submerged inside the container. The free surface of liquid is assumed to be perpendicular to axis of the container and is divided into two parts by the baffle. The method also captures the singular asymptotic behavior of the velocity potential at the sharp baffle edge. The liquid is assumed to be incompressible and inviscid and the method uses matched eigenfunction expansions and Galerkin expansions to derive unknown coefficients presented in the velocity potential series. A finite element analysis is also used to check the validity of the proposed method. The effects of some important parameters of system are also considered on the sloshing frequencies.
Low Frequency Sloshing Analysis of Cylindrical Containers with Flat and Conical Baffles
International Journal of Applied Mechanics and Engineering, 2017
This paper presents an analysis of low-frequency liquid vibrations in rigid partially filled containers with baffles. The liquid is supposed to be an ideal and incompressible one and its flow is irrotational. A compound shell of revolution is considered as the container model. For evaluating the velocity potential the system of singular boundary integral equations has been obtained. The single-domain and multi-domain reduced boundary element methods have been used for its numerical solution. The numerical simulation is performed to validate the proposed method and to estimate the sloshing frequencies and modes of fluid-filled cylindrical shells with baffles in the forms of circular plates and truncated cones. Both axisymmetric and non-axisymmetric modes of liquid vibrations in baffled and un-baffled tanks have been considered. The proposed method makes it possible to determine a suitable place with a proper height for installing baffles in tanks by using the numerical experiment.
Journal of Fluids and Structures, 2010
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.
Ocean Engineering, 2020
Dynamic response and free vibration analysis of stiffened shells having parabolic curvatures, with applications to ships and other similar structures are the main focus of this study. The energy approach is employed to the determination of equivalent orthotropic shell parameters of parabolic stiffened shells. The unstiffened equivalent shell has proper accuracy in predicting free vibration characteristics as well as dynamic response of the main stiffened shell. Reducing the governing equation difficulties with suitable precision in free vibration and dynamic response analyses is the most advantage of replacement of stiffened shells with their unstiffened equivalences.
BEM in free vibration analysis of elastic shells coupled with liquid sloshing
WIT transactions on modelling and simulation, 2015
This paper deals with the fluid-structure interaction analysis of a shell partially filled with a liquid. The shell is considered to be thin and the Kirghoff-Lave linear theory hypotheses are applied. The liquid is ideal and incompressible. The problem of analysing the dynamics of shells of revolution partially filled with an ideal incompressible liquid was reduced to solving the system of singular integral equations. The solution was obtained by using a coupled BEM and FEM in-house solver. The tank structure is modelled by the FEM and the liquid sloshing in the fluid domain is described by the BEM. The shell vibrations coupled with liquid sloshing under the force of gravity were considered. The shell and sloshing modes were analysed simultaneously. The free vibration analysis of the elastic cylindrical shell was carried out using the proposed techniques.
European Journal of Mechanics-A/Solids, 2010
An analytical method is developed to consider the free vibration of an elastic bottom plate of a partially fluid-filled cylindrical rigid container with an internal body. The internal body is a rigid cylindrical block that is concentrically and partially submerged inside the container. The developed method captured the analytical features of the velocity potential in a non-convex, continuous, and simply connected fluid domain including the interaction between the fluid and the structure. The interaction between the fluid and the bottom plate is included. The Galerkin method is used for matching the velocity potentials appropriate to two distinct fluid regions across the common horizontal boundary (artificial horizontal boundary). Then, the Rayleigh–Ritz method is also used to calculate the natural frequencies and modes of the bottom plate of the container. The results obtained for the problem without internal body are in close agreement with both experimental and numerical results a...
Analytical and experimental investigation on vibrating membranes with a central point support
Journal of Sound …, 1999
This investigation arose from the practical necessity of placing a centrifugal pump rigidly attached to a thin, circular cover plate of a water tank in a medium size ocean vessel. Due to lack of space, it was necessary to locate the system off-center of the circular configuration. It was considered necessary to calculate the fundamental frequency of the coupled system.