Flow-Induced Vibration of Anisotropic Cylindrical Shells

2002 ◽  
Author(s):  
M. H. Toorani ◽  
A. A. Lakis
Keyword(s):  
Natural Frequencies ◽  
Cylindrical Shells ◽  
Fluid Pressure ◽  
Coupled System ◽  
Flow Induced Vibration ◽  
Critical Flow Velocity ◽  
Flowing Fluid ◽  
Coupled Equations ◽  
Stiffness Matrices ◽  
Analytical Integration

This paper deals with the vibration analysis of anisotropic laminated cylindrical shells conveying fluid. We focus on the axi-symmetric (n=0) and lateral (beam-like, n=1) vibration modes of the anisotropic cylindrical shells. Particularly important in this study is to obtain the natural frequencies of the fluid-structure coupled system and also to estimate the critical flow velocity at which the structure loses its stability. The coupled equations between the shell and the fluid are derived from a refined shell theory by taking into account the shear deformation effects. The displacement functions are obtained from the exact solution of refined shell equations and therefore the mass and stiffness matrices of the shell are determined by precise analytical integration. The added mass, stiffness and damping matrices of the fluid are obtained by an analytical integration of the fluid pressure over the liquid element. Thereafter, these matrices are coupled with the dynamic equation of the empty shell. The natural frequencies obtained with the shell partially or completely filled with liquid are in good agreement with those obtained experimentally and from other theories. The stability of the shell subjected to a flowing fluid is also studied. The shell’s anisotropy is discussed.

Response of Fluid-Elastically Coupled Coaxial Cylindrical Shells to External Flow

1977 ◽  
Vol 99 (2) ◽  
pp. 319-324 ◽  
Author(s):  
M. K. Au-Yang
Keyword(s):  
Vibration Analysis ◽  
Natural Frequencies ◽  
Numerical Solutions ◽  
Dynamic Pressure ◽  
Equations Of Motion ◽  
Cylindrical Shells ◽  
Axial Flow ◽  
Coupled System ◽  
Coupling Coefficients ◽  
Coupled Equations

The dynamics of a system of two fluid-elastically coupled coaxial cylindrical shells is studied theoretically. The general equations of motion for free and forced-damped vibration are derived in terms of virtual mass, coupling coefficients, and uncoupled natural frequencies of the individual cylindrical shells. For free vibration, numerical solutions to the coupled equations of motion are given as a function of these parameters. For forced-damped vibration, solution is given to the special case when the external force is a normal one acting on the surface of the outer shell, such as the dynamic pressure forces arising from an external turbulent axial flow. It is shown that the coupled system can then be reduced to an equivalent single cylindrical shell. However, the effective force acting on the equivalent single cylinder, as well as its natural frequencies and effective damping ratios, are all modified from the corresponding uncoupled values. The response of the system can then be predicted by established methods in flow-induced random vibration analysis. Curves are included. The study aims mainly at applications to the vibration analysis of hydraulically coupled internal components of a pressurized nuclear reactor but is general enough to find application in other engineering disciplines.

Annular Axial Flow-Induced Vibration of Cylindrical Shells by Flu¨gge’s Shell Theory

2006 ◽  
Author(s):  
Katsuhisa Fujita ◽  
Makoto Katou
Keyword(s):  
Shell Theory ◽  
Stokes Equations ◽  
Cylindrical Shells ◽  
Axial Flow ◽  
Navier Stokes ◽  
Complex Eigenvalue ◽  
Flow Induced Vibration ◽  
Navier Stokes Equations ◽  
Flowing Fluid ◽  
Narrow Passage

The unstable phenomena of thin cylindrical shells subjected to annular axial flow are investigated. In this paper, the analytical model is composed of an elastic axisymmetric shell and a rigid one which are arranged co-axially. Considering the fluid structure interaction between shells and fluid flowing through an annular narrow passage, the coupled equation of motion is derived using Flu¨gge’s shell theory and Navier-Stokes equations. The unstable phenomena of thin cylindrical shells are clarified by using the root locus based on the complex eigenvalue analysis. The numerical parameter studies on the shells with a freely supported end and a rigid one, and with both simply supported ends, are performed taking the dimensins of shells, the characteristics of flowing fluid so on as parameters. The influence of these parameters on the threshold of instability of the coupled vibration between thin cylindrical shells and annular axial flowing fluid are investigated and discussed.

Axial Leakage Flow-Induced Vibration of Thin Cylindrical Shell With Respect to Circumferential Vibration

2002 ◽  
Author(s):  
Katsuhisa Fujita ◽  
Atsuhiko Shintani ◽  
Masakazu Ono
Keyword(s):  
Cylindrical Shell ◽  
Equations Of Motion ◽  
Fluid Pressure ◽  
Navier Stokes ◽  
Leakage Flow ◽  
Thin Cylindrical Shell ◽  
Flow Induced Vibration ◽  
Navier Stokes Equation ◽  
Coupled Equations ◽  
Unstable Vibration

In this paper, the dynamic stability of a thin cylindrical shell subjected to axial leakage flow is discussed. In this paper, the third part of a study of the axial leakage flow-induced vibration of a thin cylindrical shell, we focus on circumferential vibration, that is, the ovaling vibration of a shell. The coupled equations of motion between shell and liquid are obtained by using Donnell’s shell theory and the Navier-Stokes equation. The added mass, added damping and added stiffness in the coupled equations of motion are described by utilizing the unsteady fluid pressure acting on the shell. The relations between axial velocity and the unstable vibration phenomena are clarified concerning the circumferential vibration of a shell. Numerical parametric studies are done for various dimensions of a shell and an axial leakage flow.

Axial Leakage Flow-Induced Vibration of a Thin Cylindrical Shell With Respect to Axisymmetric Vibration

2003 ◽  
Vol 125 (2) ◽  
pp. 151-157 ◽  
Author(s):  
Katsuhisa Fujita ◽  
Atsuhiko Shintani ◽  
Masakazu Ono
Keyword(s):  
Cylindrical Shell ◽  
Axial Flow ◽  
Navier Stokes ◽  
Leakage Flow ◽  
Axisymmetric Vibration ◽  
Thin Cylindrical Shell ◽  
Flow Induced Vibration ◽  
Navier Stokes Equation ◽  
Coupled Equations ◽  
Stiffness Matrices

In this paper, the stability of a thin cylindrical shell subjected to axial leakage flow is discussed. In this paper, the first part of a study of the axial leakage flow-induced vibration of a thin cylindrical shell, we focus on axisymmetric vibration, that is, the ringlike vibration of a shell. The coupled equations between a shell and a fluid are obtained by using the Donnell’s shell theory and the Navier-Stokes equation. The added mass, added damping and added stiffness matrices in the coupled equations are described by utilizing unsteady fluid forces on a shell. The influence of the axial flow velocity on the unstable phenomena is clarified concerning axisymmetric vibration mode of shell. The numerical calculations are performed taking the dimensions of shell and fluid as parameters.

Theoretical Analysis of Free Vibrations Based on a New High Order Shell Theory for Cylindrical Shells Conveying Fluid

2017 ◽  
Author(s):  
Ming Ji ◽  
Kazuaki Inaba
Keyword(s):  
Boundary Conditions ◽  
Shell Theory ◽  
Natural Frequencies ◽  
Equations Of Motion ◽  
Cylindrical Shells ◽  
Fluid Pressure ◽  
Free Vibrations ◽  
High Order ◽  
Out Of Plane ◽  
Conveying Fluid

The natural frequencies of free vibrations for thick cylindrical shells with clamped-clamped ends conveying fluid are investigated. Equations of motion and boundary conditions are derived by Hamilton’s principle based on the new high order shell theory. The hydrodynamic force is derived from the linearized potential flow theory. Besides, fluid pressure acting on the shell wall is gotten by the assumption of non-penetration condition. The out-of-plane and in-plane vibrations are coupled together due to the existence of fluid-solid-interaction (FSI). Under the assumption of harmonic motion, the dispersion relationships are presented. Using the method of frequency sweeping, the natural frequencies of symmetric modes and asymmetric modes corresponding to each flow velocity are found by satisfying the dispersion relationship equations and boundary conditions. Several numerical examples with different flow velocities and thickness are presented compared with previous thin shell theory and FEM results and show reasonable agreement. The effects of thickness are discussed.

Non-Linear Fluid-Structure Interaction in Cylindrical Shells

2002 ◽  
Author(s):  
M. H. Toorani ◽  
A. A. Lakis
Keyword(s):  
Natural Frequencies ◽  
Cylindrical Shells ◽  
Axial Flow ◽  
Present Theory ◽  
Nuclear Plant ◽  
Nuclear Industry ◽  
Linear Potential ◽  
Critical Flow Velocity ◽  
Fluid Structure ◽  
Non Linear

Nuclear plant reliability depends directly on its component performance. The higher heat transfer performance of nuclear plant components often requires higher flow velocities through the shell and tube heat exchangers. So, these cylindrical structures are subjected to either axial or cross flow, while the excessive flow-induced vibrations, (which are a major cause of machinery downtime; fatigue failure and high noise), limit the performance of these structures. On the other hand, these shell components often experience large amplitude vibrations that are greater than the shell thickness. Therefore, the evaluation of complex vibrational behavior of these structures is highly desirable in the nuclear industry. A semi-analytical approach has been developed in the present theory to predict the geometrical non-linearity influence on the natural frequencies of anisotropic cylindrical shells conveying axial flow. Particular important in this study is to obtain the natural frequencies of the coupled system of the fluid-structure, taking into account the geometrical non-linearity of the structure, and also estimating the critical flow velocity at which the structure loses its stability. The displacement functions, mass and stiffness matrices, linear and non-linear ones, of the structure are obtained by exact analytical integration over a hybrid element developed in this work. Linear potential flow theory is applied to describe the fluid effect that leads to the inertial, centrifugal and Coriolis forces. Numerical results are given and compared with those of experiment and other theories to demonstrate the practical application of the present method.

Dynamic Analysis of Anisotropic Cylindrical Shells Containing Flowing Fluid

2001 ◽  
Vol 123 (4) ◽  
pp. 454-460 ◽  
Author(s):  
M. H. Toorani ◽  
A. A. Lakis
Keyword(s):  
Transverse Shear ◽  
Equations Of Motion ◽  
Cylindrical Shells ◽  
Fluid Pressure ◽  
Laminated Composite ◽  
Present Theory ◽  
Curvilinear Coordinates ◽  
Structural Element ◽  
Flowing Fluid ◽  
Bernoulli’S Equation

This paper deals with the study of dynamic behavior of anisotropic cylindrical shells, based on refined shell theory, subjected simultaneously to an internal and external fluid. In the present theory, the transverse shear deformation effect is taken into account, therefore, the equations of motion are determined with displacements and transverse shear as independent variables. The solution is divided into three parts: In Section 2, the displacement functions are derived from the exact solution of refined shell equations based on orthogonal curvilinear coordinates. The mass and stiffness matrices of each structural element are derived by exact analytical integration. In Section 3, the velocity potential, Bernoulli’s equation and impermeability condition have been applied to the shell fluid interface to obtain an explicit expression for fluid pressure which yields three forces (inertial, centrifugal, Coriolis). Numerical examples are given in Section 4 for the free vibration of laminated composite and isotropic materials for both open and closed circular cylindrical shells. Reasonable agreement is found with other theories and experiments.

Flow-Induced Vibration: Guidelines for Design, Diagnosis, and Troubleshooting of Common Power Plant Components

1985 ◽  
Vol 107 (4) ◽  
pp. 326-334 ◽  
Author(s):  
M. K. Au-Yang
Keyword(s):  
Power Plant ◽  
Vortex Shedding ◽  
Cylindrical Shells ◽  
Leakage Flow ◽  
Flat Plates ◽  
Flow Induced Vibration ◽  
Flowing Fluid ◽  
Vibration Problems ◽  
Tube Banks ◽  
Plant Components

The different techniques of assessing the flow-induced vibration problems of common power plant components are reviewed. The components are divided into categories of single cylinders, flat plates, pipes containing flowing fluid, cylindrical shells, and tube banks. The mechanisms considered include turbulent buffeting, instability, vortex shedding, acoustics, and leakage flow-induced vibration. Emphasis is placed on applications to industrial problems.

scholarly journals Dynamic Analysis Technique of Rotating Centrifugal Impeller

1991 ◽  
Author(s):  
Jin Zhang ◽  
X. J. Chen ◽  
W. L. Wang
Keyword(s):  
Experimental Data ◽  
Dynamic Analysis ◽  
Natural Frequencies ◽  
Coupled System ◽  
Economic Benefits ◽  
Centrifugal Impeller ◽  
Stiffness Matrices ◽  
Analysis Technique ◽  
Reduced Coordinates ◽  
Made In

A dynamic analysis technique which can be employed in rotating centrifugal impeller is presented in this paper. It shows that multi–component partition can be made in repetitive sector region of the centrifugal impeller. The basic repectivie sector region of the centrifugal impeller is divided into three substructures: the full blade, the short blade and the sectorial part of the disc. By using Benfield mode substitution combined with group transformation successfully, the Hermite generalized mass and stiffness matrices under the reduced coordinates are derived. From this, the natural frequencies and the corresponding modal shapes of the bladed disc coupled system can be solved. The comparison of the analytical results obtained by using this method, other methods and the experimental data of models verifies the reliability, practicability and considerable economic benefits of the method presented in this paper.

LIQUID-DIAPHRAGM INTERACTION OF MICROPUMP

2005 ◽  
Vol 19 (28n29) ◽  
pp. 1667-1670
Author(s):  
JIANKANG WU ◽  
LIJUN LU
Keyword(s):  
Natural Frequencies ◽  
Fluid Pressure ◽  
Coupled System ◽  
Mode Analysis ◽  
Water Model ◽  
Shallow Water Model ◽  
Vibration Equation ◽  
First Order ◽  
Rate Frequency ◽  
Coupled Equation

This paper employs a thickness-averaged shallow water model to approximate periodical flows in a piezoelectric micropump. The fluid pressure equation is combined with the vibration equation of silicon diaphragm to construct a liquid-solid coupled equation. Numerical results of mode analysis of the coupled system indicate that the natural frequencies of coupled system are much lower than those of the non-coupled system. The relationships of the first order amplitude-frequency of the silicon diaphragm, and the flow rate-frequency of micropump are also given in this paper.

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