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 Stability Analysis of Cans in Reactor Coolant Pump Subjected to Axial Flow

2014 ◽  
Author(s):  
Wenbo Ning ◽  
Dezhong Wang
Keyword(s):  
Dynamic Stability ◽  
Cylindrical Shells ◽  
Axial Flow ◽  
Geometrical Parameters ◽  
Coolant Pump ◽  
Critical Flow Velocity ◽  
Reactor Coolant ◽  
Annular Gap ◽  
The Stability ◽  
Canned Motor

The stator and rotor cans in canned motor reactor coolant pump are assumed to be elastic coaxial cylindrical shells due to their particular geometric structures in present study. Thin shell structures such as cans are prone to buckling instabilities. Furthermore, a lot of accidents were caused by losing stability. The dynamic behavior of coaxial circular cylindrical shells subjected to axial fluid flow in the annular gap between two shells is investigated in this paper. The outer shell is stiffened by ring-ribs because of its instability easily. The shell is modeled based on Donnell’s shallow theory. The “smeared stiffeners” approach is used for ring-stiffeners. The fluid is assumed to be an incompressible ideal fluid and the potential flow theory is employed to describe shell-fluid interaction. Numerical analyses are conducted by means of energy variation to obtain the critical flow velocity of losing stability with aid of Hamilton principle. This study shows effects of geometrical parameters on stability of shells. The size and number of ring-stiffeners on dynamic stability are examined. It is found that stiffeners can vary modes instability and enhance the stability of shells. The flow velocities of losing stability with different boundary conductions can be calculated and compared. The results show clamped shells are more stable than simply supported shells. The results presented are in reasonable agreement with those available in the literature.

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.

scholarly journals Non-linear Vibrations of Deep Cylindrical Shells by thep-Version Finite Element Method

2010 ◽  
Vol 17 (1) ◽  
pp. 21-37 ◽  
Author(s):  
Pedro Ribeiro ◽  
Bruno Cochelin ◽  
Sergio Bellizzi
Keyword(s):  
Finite Element ◽  
Degrees Of Freedom ◽  
Natural Frequencies ◽  
Numerical Study ◽  
Cylindrical Shells ◽  
Element Formulation ◽  
Fe Model ◽  
Various Boundary Conditions ◽  
Non Linear ◽  
Linear Vibrations

Ap-version shell finite element based on the so-called shallow shell theory is for the first time employed to study vibrations of deep cylindrical shells. The finite element formulation for deep shells is presented and the linear natural frequencies of different shells, with various boundary conditions, are computed. These linear natural frequencies are compared with published results and with results obtained using a commercial software finite element package; good agreement is found. External forces are applied and the displacements in the geometrically non-linear regime computed with thep-model are found to be close to the ones computed using a commercial FE package. In all numerical tests thep-FE model requires far fewer degrees of freedom than the regular FE models. A numerical study on the dynamic behaviour of deep shells is finally carried out.

Nonlinear Stability of Circular Cylindrical Shells in Annular and Unbounded Axial Flow

2001 ◽  
Vol 68 (6) ◽  
pp. 827-834 ◽  
Author(s):  
M. Amabili ◽  
F. Pellicano ◽  
M. A. Pai¨doussis
Keyword(s):  
Boundary Conditions ◽  
Degrees Of Freedom ◽  
Cylindrical Shells ◽  
Axial Flow ◽  
Longitudinal Direction ◽  
Finite Amplitude ◽  
External Flow ◽  
Linear Potential ◽  
Circular Cylindrical Shells ◽  
The Galerkin Method

The stability of circular cylindrical shells with supported ends in compressible, inviscid axial flow is investigated. Nonlinearities due to finite-amplitude shell motion are considered by using Donnell’s nonlinear shallow-shell theory; the effect of viscous structural damping is taken into account. Two different in-plane constraints are applied at the shell edges: zero axial force and zero axial displacement; the other boundary conditions are those for simply supported shells. Linear potential flow theory is applied to describe the fluid-structure interaction. Both annular and unbounded external flow are considered by using two different sets of boundary conditions for the flow beyond the shell length: (i) a flexible wall of infinite extent in the longitudinal direction, and (ii) rigid extensions of the shell (baffles). The system is discretized by the Galerkin method and is investigated by using a model involving seven degrees-of-freedom, allowing for traveling-wave response of the shell and shell axisymmetric contraction. Results for both annular and unbounded external flow show that the system loses stability by divergence through strongly subcritical bifurcations. Jumps to bifurcated states can occur well before the onset of instability predicted by linear theory, showing that a linear study of shell stability is not sufficient for engineering applications.

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.

Nonlinear Stability of Circular Cylindrical Shells in Axially Flowing Fluid

2000 ◽  
Author(s):  
M. Amabili ◽  
M. P. Païdoussis ◽  
F. Pellicano
Keyword(s):  
Boundary Conditions ◽  
Degrees Of Freedom ◽  
Cylindrical Shells ◽  
Axial Flow ◽  
Longitudinal Direction ◽  
Travelling Wave ◽  
External Flow ◽  
Linear Potential ◽  
Flowing Fluid ◽  
Circular Cylindrical Shells

Abstract The stability of supported, circular cylindrical shells in compressible, inviscid axial flow is investigated. Nonlinearities due to large amplitude shell motion are considered by using the nonlinear Donnell shallow shell theory and the effect of viscous structural damping is taken into account. Two different in-plane constraints are applied to the shell edges: zero axial force and zero axial displacement; the other boundary conditions are those for simply supported shells. Linear potential flow theory is applied to describe the fluid-structure interaction. Both annular and unbounded external flow are considered by using two different sets of boundary conditions for the flow beyond the shell length: (i) a flexible wall of infinite extent in the longitudinal direction, and (ii) rigid extensions of the shell (baffles). The system is discretised by Galerkin projections and is investigated by using a model involving seven degrees of freedom, allowing for travelling wave response of the shell and shell axisymmetric contraction. Results for both annular and unbounded external flow show that the system loses stability by divergence through strongly subcritical bifurcations. Jumps to bifurcated positions can happen much before the onset of instability predicted by linear theories, showing the necessity of a nonlinear study.

Linear and non-linear potential-flow calculations of free-surface waves with lift and induced drag

2000 ◽  
Vol 214 (6) ◽  
pp. 801-812
Author(s):  
C-E Janson
Keyword(s):  
Free Surface ◽  
Potential Flow ◽  
Lift Force ◽  
Radiation Condition ◽  
Linear Potential ◽  
Surface Boundary ◽  
Model Approximation ◽  
Non Linear ◽  
Lifting Surfaces ◽  
The Waves

A potential-flow panel method is used to compute the waves and the lift force from surface-piercing and submerged bodies. In particular the interaction between the waves and the lift produced close to the free surface is studied. Both linear and non-linear free-surface boundary conditions are considered. The potential-flow method is of Rankine-source type using raised source panels on the free surface and a four-point upwind operator to compute the velocity derivatives and to enforce the radiation condition. The lift force is introduced as a dipole distribution on the lifting surfaces and on the trailing wake, together with a flow tangency condition at the trailing edge of the lifting surface. Different approximations for the spanwise circulation distribution at the free surface were tested for a surface-piercing wing and it was concluded that a double-model approximation should be used for low speeds while a single-model, which allows for a vortex at the free surface, was preferred at higher speeds. The lift force and waves from three surface-piercing wings, a hydrofoil and a sailing yacht were computed and compared with measurements and good agreement was obtained.

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