Vibration and Stability of Cylindrical Shells Containing Flowing Fluid

2002 ◽  
Author(s):  
Igor Zolotarev
Keyword(s):  
Cylindrical Shell ◽  
Boundary Conditions ◽  
Finite Length ◽  
Natural Frequencies ◽  
Critical Flow ◽  
Thin Shells ◽  
Fluid Viscosity ◽  
Critical Flow Velocity ◽  
Flowing Fluid ◽  
The Stability

Natural frequencies and the thresholds for loosing the stability of thin-walled cylindrical shell conveying by flowing fluid are theoretically studied. Potential flow theory for fluid and 3D theory for thin shells are used. The shells of finite length are considered for the different case of boundary conditions at the edges of the shell, and their influence on the critical flow velocities for flutter are demonstrated. The fundamental importance of boundary conditions considered for fixing the edges of the cylindrical shell of finite length is shown. When the clamped - simply supported boundary conditions are assumed, the critical flow velocity for flutter is very low, even if the energy dissipation due to the fluid viscosity was taken into account.

scholarly journals Strain Growth in a Finite-Length Cylindrical Shell Under Internal Pressure Pulse

2017 ◽  
Vol 139 (2) ◽  
Author(s):  
Qi Dong ◽  
Q. M. Li ◽  
Jinyang Zheng
Keyword(s):  
Cylindrical Shell ◽  
Boundary Conditions ◽  
Internal Pressure ◽  
Finite Length ◽  
Pressure Pulse ◽  
Elastic Response ◽  
Local Dynamic ◽  
Growth Phenomenon ◽  
Modal Coupling ◽  
Elastic Responses

Strain growth is a phenomenon observed in the elastic response of containment vessels subjected to internal blast loading. The local dynamic response of a containment vessel may become larger in a later stage than its response in the earlier stage. In order to understand the possible mechanisms of the strain growth phenomenon in a cylindrical vessel, dynamic elastic responses of a finite-length cylindrical shell with different boundary conditions subjected to internal pressure pulse are studied by finite-element simulation using LS-DYNA. It is found that the strain growth in a finite-length cylindrical shell with sliding–sliding boundary conditions is caused by nonlinear modal coupling. Strain growth in a finite-length cylindrical shell with free–free or simply supported boundary conditions is primarily caused by the linear modal superposition, possibly enhanced by the nonlinear modal coupling. The understanding of these strain growth mechanisms can guide the design of cylindrical containment vessels.

scholarly journals Wave Based Method for Free Vibration Analysis of Ring Stiffened Cylindrical Shell with Intermediate Large Frame Ribs

2013 ◽  
Vol 20 (3) ◽  
pp. 459-479 ◽  
Author(s):  
Meixia Chen ◽  
Jianhui Wei ◽  
Kun Xie ◽  
Naiqi Deng ◽  
Guoxiang Hou
Keyword(s):  
Cylindrical Shell ◽  
Free Vibration ◽  
Boundary Conditions ◽  
Natural Frequencies ◽  
Free Vibration Analysis ◽  
Structure Type ◽  
Vibration Characteristics ◽  
Mode Shapes ◽  
Arbitrary Boundary ◽  
Stiffened Cylindrical Shell

Wave based method which can be recognized as a semi-analytical and semi-numerical method is presented to analyze the free vibration characteristics of ring stiffened cylindrical shell with intermediate large frame ribs for arbitrary boundary conditions. According to the structure type and the positions of discontinuities, the model is divided into different substructures whose vibration field is expanded by wave functions which are exactly analytical solutions to the governing equations of the motions of corresponding structure type. Boundary conditions and continuity equations between different substructures are used to form the final matrix to be solved. Natural frequencies and vibration mode shapes are calculated by wave based method and the results show good agreement with finite element method for clamped-clamped, shear diaphragm – shear diaphragm and free-free boundary conditions. Free vibration characteristics of ring stiffened cylindrical shells with intermediate large frame ribs are compared with those with bulkheads and those with all ordinary ribs. Effects of the size, the number and the distribution of intermediate large frame rib are investigated. The frame rib which is large enough is playing a role as bulkhead, which can be considered imposing simply supported and clamped constraints at one end of the cabin and dividing the cylindrical shell into several cabins vibrating separately at their own natural frequencies.

Dynamic Stability of Isotropic or Composite-Material Cylindrical Shells Containing Swirling Fluid Flow

1977 ◽  
Vol 44 (1) ◽  
pp. 112-116 ◽  
Author(s):  
T. L. C. Chen ◽  
C. W. Bert
Keyword(s):  
Shell Theory ◽  
Swirling Flow ◽  
Circular Cylindrical Shell ◽  
Critical Flow ◽  
Fluid System ◽  
Critical Flow Velocity ◽  
Rotating Speed ◽  
Fluid Forces ◽  
Shell Motion ◽  
The Stability

A linear stability analysis is presented for a thin-walled, circular cylindrical shell of orthotropic material conveying a swirling flow. Shell motion is modeled by using the dynamic orthotropic version of the Sanders shell theory and fluid forces are described by inviscid, incompressible flow theory. The critical flow velocities are determined for piping made of composite and isotropic materials conveying swirling water. Fluid rotation strongly degrades the stability of the shell/fluid system, i.e. increasing the fluid rotating speed severely decreases the critical flow velocity.

scholarly journals Wettability and confinement size effects on stability of water conveying nanotubes

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
M. Shaat ◽  
U. Javed ◽  
S. Faroughi
Keyword(s):  
Size Effects ◽  
Natural Frequencies ◽  
Applied Pressure ◽  
Surface Wettability ◽  
Fluid Viscosity ◽  
Nanoconfined Water ◽  
Water Viscosity ◽  
The Stability ◽  
Stability Of Water ◽  
Ice Shell

Abstract This study investigates the wettability and confinement size effects on vibration and stability of water conveying nanotubes. We present an accurate assessment of nanotube stability by considering the exact mechanics of the fluid that is confined in the nanotube. Information on the stability of nanotubes in relation to the fluid viscosity, the driving force of the fluid flow, the surface wettability of the nanotube, and the nanotube size is missing in the literature. For the first time, we explore the surface wettability dependence of the nanotube natural frequencies and stability. By means of hybrid continuum-molecular mechanics (HCMM), we determined water viscosity variations inside the nanotube. Nanotubes with different surface wettability varying from super-hydrophobic to super-hydrophilic nanotubes were studied. We demonstrated a multiphase structure of nanoconfined water in nanotubes. Water was seen as vapor at the interface with the nanotube, ice shell in the middle, and liquid water in the nanotube core. The average velocity of water flow in the nanotube was obtained strongly depend on the surface wettability and the confinement size. In addition, we report the natural frequencies of the nanotube as functions of the applied pressure and the nanotube size. Mode divergence and flutter instabilities were observed, and the activation of these instabilities strongly depended on the nanotube surface wettability and size. This work gives important insights into understanding the stability of nanotubes conveying fluids depending on the operating pressures and the wettability and size of confinement. We revealed that hydrophilic nanotubes are generally more stable than hydrophobic nanotubes when conveying fluids.

The Stability of Plane Poiseuille Flow in a Finite-Length Channel

2021 ◽  
Author(s):  
Lei Xu ◽  
Zvi Rusak
Keyword(s):  
Kinetic Energy ◽  
Boundary Conditions ◽  
Linear Stability ◽  
Finite Length ◽  
Poiseuille Flow ◽  
Weak Form ◽  
Plane Poiseuille Flow ◽  
Various Boundary Conditions ◽  
New Perspective ◽  
The Stability

Abstract The linear stability of plane Poiseuille flow through a finite-length channel is studied. A weakly-divergence-free basis finite element method with SUPG stabilization is used to formulate the weak form of the problem. The linear stability characteristics are studied under three possible inlet-outlet boundary conditions and the corresponding perturbation kinetic energy transfer mechanisms are investigated. Active transfer of perturbation kinetic energy at the channel inlet and outlet, energy production due to convection and dissipation at the flow bulk provide a new perspective in understanding the distinct stability characteristics of plane Poiseuille flow under various boundary conditions.

The Dynamics of MEMS Arches of Non-Ideal Boundary Conditions

2011 ◽  
Author(s):  
Sami A. Alkharabsheh ◽  
Mohammad I. Younis
Keyword(s):  
Boundary Conditions ◽  
Natural Frequencies ◽  
Electrostatic Force ◽  
Dynamical Behavior ◽  
Experimental Investigations ◽  
Harmonic Load ◽  
Ideal Boundary ◽  
Shooting Technique ◽  
Softening Behavior ◽  
The Stability

We present an investigation into the dynamics of MEMS arches when actuated electrically including the effect of their flexible (non-ideal) supports. First, the eigenvalue problem of a nonlinear Euler-Bernoulli shallow arch with torsional and transversal springs at the boundaries is solved analytically. Several results are shown to demonstrate the possibility of tuning the theoretically obtained natural frequencies of an arch to match the experimentally measured. Then, simulation results are shown for the forced vibration response of an arch when excited by a DC electrostatic force superimposed to an AC harmonic load. Shooting technique is utilized to find periodic motions. The stability of the captured periodic motion is examined using the Floquet theory. The results show several jumps in the response during snap-through motion and pull-in. Theoretical and experimental investigations are conducted on a microfabricated curved beam actuated electrically. Results show softening behavior and superharmonic resonances. It is demonstrated that non-ideal boundary conditions can have significant effect on the qualitative dynamical behavior of the MEMS arch, including its natural frequencies, snap-through behavior, and dynamic pull-in.

Effect of Winkler and Pasternak elastic foundation on the vibration of rotating functionally graded material cylindrical shell

2018 ◽  
Vol 232 (24) ◽  
pp. 4564-4577 ◽  
Author(s):  
Muzamal Hussain ◽  
Muhammad Nawaz Naeem ◽  
Mohammad Reza Isvandzibaei
Keyword(s):  
Cylindrical Shell ◽  
Boundary Conditions ◽  
Elastic Foundation ◽  
Natural Frequencies ◽  
Cylindrical Shells ◽  
Functionally Graded ◽  
Radius Ratio ◽  
Wave Number ◽  
Simply Supported ◽  
Elastic Foundations

In this paper, vibration characteristics of rotating functionally graded cylindrical shell resting on Winkler and Pasternak elastic foundations have been investigated. These shells are fabricated from functionally graded materials. Shell dynamical equations are derived by using the Hamilton variational principle and the Langrangian functional framed from the shell strain and kinetic energy expressions. Elastic foundations, namely Winkler and Pasternak moduli are inducted in the tangential direction of the shell. The rotational motions of the shells are due to the Coriolis and centrifugal acceleration as well as the hoop tension produced in the rotating case. The wave propagation approach in standard eigenvalue form has been employed in order to derive the characteristic frequency equation describing the natural frequencies of vibration in rotating functionally graded cylindrical shell. The complex exponential functions, with the axial modal numbers that depend on the boundary conditions stated at edges of a cylindrical shell, have been used to compute the axial modal dependence. In our new investigation, frequency spectra are obtained for circumferential wave number, length-to-radius ratio, height-to-radius ratio with simply supported–simply supported and clamped–clamped boundary conditions without elastic foundation. Also, the effect of elastic foundation on the rotating cylindrical shells is examined with the simply supported–simply supported edge. To check the validity of the present method, the fundamental natural frequencies of non-rotating isotropic and functionally graded cylindrical shells are compared with the open literature. Also, a comparison is made for infinitely long rotating with the earlier published paper.

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.

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