EXACT EIGEN-RELATIONS OF CLAMPED-CLAMPED AND SIMPLY SUPPORTED PIPES CONVEYING FLUIDS

2012 ◽  
Vol 04 (03) ◽  
pp. 1250035 ◽  
Author(s):  
PIN LU ◽  
HONGYU SHENG
Keyword(s):  
Boundary Conditions ◽  
Dynamic Stability ◽  
Dynamic Properties ◽  
Pipe Conveying Fluid ◽  
Simply Supported ◽  
Pipeline Systems ◽  
Benchmark Solutions ◽  
Conveying Fluid ◽  
Flow Velocities

The exact eigen-equations of pipe conveying fluid with clamped-clamped and simply supported boundary conditions are derived. The simplified forms of the general eigen-equations for some specific cases are determined, and the corresponding dynamic properties are calculated and discussed. These properties provide a better understanding on the relationships between the dynamic stability and the flow velocities of the fluid-conveying components and help to design stable pipeline systems. In addition, the dynamic properties obtained by the exact eigen-equations can also serve as benchmark solutions for verifying results obtained by other approximate approaches.

Effects of Shearing Loads and In-Plane Boundary Conditions on the Stability of Thin Tubes Conveying Fluid

1979 ◽  
Vol 46 (4) ◽  
pp. 779-783 ◽  
Author(s):  
J. Tani ◽  
H. Doki
Keyword(s):  
Boundary Conditions ◽  
Fourier Integral ◽  
Integral Theory ◽  
Plane Boundary ◽  
Simply Supported ◽  
Thin Walled ◽  
Shell Equation ◽  
Divergence Velocity ◽  
The Stability ◽  
Conveying Fluid

The hydroelastic stability of short, simply supported, thin-walled tubes conveying fluid is examined with an emphasis on the effects of shearing loads and in-plane boundary conditions. The Donnell shell equation is used in conjunction with linearized, potential flow theory. The solution is obtained by using Fourier integral theory and Galerkin’s method. It is found that an increase of the shearing load reduces the critical divergence velocity and raises the corresponding number of circumferential waves. A change in the in-plane boundary conditions exerts the significant effect on the critical divergence velocity of short tubes.

Exact Solutions for Vibration of Multi-Span Rectangular Mindlin Plates

2002 ◽  
Vol 124 (4) ◽  
pp. 545-551 ◽  
Author(s):  
Y. Xiang ◽  
G. W. Wei
Keyword(s):  
Boundary Conditions ◽  
Exact Solutions ◽  
Analytical Approach ◽  
Solution Method ◽  
Plate Boundary ◽  
Vibration Frequencies ◽  
Type Solution ◽  
Simply Supported ◽  
Space Technique ◽  
Benchmark Solutions

This paper presents the first-known exact solutions for the vibration of multi-span rectangular Mindlin plates with two opposite edges simply supported. The Levy type solution method and the state-space technique are employed to develop an analytical approach to deal with the vibration of rectangular Mindlin plates of multiple spans. Exact vibration frequencies are obtained for two-span square Mindlin plates with varying span ratios and two-, three- and four-equal-span rectangular Mindlin plates. The influence of the span ratios, the number of spans and plate boundary conditions on the vibration behavior of square and rectangular Mindlin plates is examined. The presented exact vibration results may serve as benchmark solutions for such plates.

Dynamics and Stability of Pinned-Free Micropipes Conveying Fluid

2017 ◽  
Vol 34 (4) ◽  
pp. 533-539 ◽  
Author(s):  
K. Hu ◽  
H. L. Dai ◽  
L. Wang ◽  
Q. Qian
Keyword(s):  
Free Boundary ◽  
Boundary Conditions ◽  
Flow Velocity ◽  
Differential Quadrature Method ◽  
Dynamical Behavior ◽  
Mass Ratio ◽  
Restoring Force ◽  
Free Boundary Conditions ◽  
Conveying Fluid ◽  
Flow Velocities

AbstractIn this paper, the dynamical behavior and stability of hanging micropipes conveying fluid with pinned-free boundary conditions are investigated. For a pinned-free rigid micropipe, the dynamical system is found to be stable for various flow velocities. Particular emphasis is placed on the effects of flow velocity, mass ratio and gravity on the dynamics and flutter instability of flexible micropipe system with pinned-free boundary conditions. The governing equations for flexible micropipes are discretized using the differential quadrature method (DQM), yielding a generalized eigenvalue problem which is then solved for various flow velocities, mass ratios and gravity parameters. It is shown that, with increasing flow velocity, the flexible micropipe with pinned-free boundary conditions is stable until it becomes unstable via a Hopf bifurcation leading to flutter. The system may lose stability first in the second or third mode, mainly depending on the selected value of mass ratio. The existence of mode exchange between the second and third modes is possible. The gravity parameter of positive values causes additional restoring force and hence enhances the stability of the micropipe system; however, it can generate the complexity of stability diagrams.

Transverse Free Vibration Analysis of Buried Pipeline under Simply Supported Restraint

2012 ◽  
Vol 446-449 ◽  
pp. 2210-2213
Author(s):  
Ting Yue Hao
Keyword(s):  
Vibration Analysis ◽  
Vibration Mode ◽  
Free Vibration Analysis ◽  
Beam Model ◽  
Pipe Conveying Fluid ◽  
Buried Pipeline ◽  
Simply Supported ◽  
Pipe Model ◽  
Elastic Foundation Beam ◽  
Conveying Fluid

The pipe model is simplified as elastic foundation beam model of Euler-Bernoulli in the paper. Considering the effect of fluid flow in the pipe and outer soil constraint, the transverse vibration differential equation of buried pipeline is derived by using of Hamilton principle. By utilization of the first three-order modal and the orthogoality of main vibration mode, the equation is deduced and transformed into state formulas. The typical numerical example is analyzed by Matlab software. It is found that the natural frequency of pipe conveying fluid usually decreases along with flow velocity improving and the effect of foundation on the pipe stability is apparent.

Parametric Resonance of Pipes with Soft and Hard Segments Conveying Pulsating Fluids

2018 ◽  
Vol 18 (10) ◽  
pp. 1850119 ◽  
Author(s):  
Qian Li ◽  
Wei Liu ◽  
Zijun Zhang ◽  
Zhufeng Yue
Keyword(s):  
Numerical Calculation ◽  
Parametric Resonance ◽  
Great Influence ◽  
Mode Shapes ◽  
Pipe Conveying Fluid ◽  
Stiffness Ratio ◽  
Mean Flow ◽  
Simply Supported ◽  
Hard Segments ◽  
Conveying Fluid

In this paper, the parametric resonance of pipes with soft and hard segments induced by pulsating fluids is investigated. The lowest six natural frequencies and mode shapes of the soft–hard combination pipe simply supported at both ends are obtained by the modified Galerkin's method. The Floquet method is used to numerically determine the parametric resonance regions, including subharmonic resonance regions and combination resonance regions. The parametric resonance results are verified by comparison with published ones, which confirm the validity of the present model establishment and numerical calculation. Compared with a uniform pipe conveying fluid simply supported at both ends, the soft–hard pipe conveying fluid is found to reveal different dynamical behaviors. Decreasing the length of the soft pipe, while increasing the stiffness ratio of the hard pipe compared to the soft one, can effectively improve the stability of the pipe system. The parametric resonance results show that the mean flow velocity and pulsation amplitude of the fluid have a great influence on the width of the parametric resonance regions. It is advisable that the ratio (the soft pipe/the whole pipe) of the length may be designed to be 0.4–0.5 for a flexural rigidity ratio (the hard pipe/the soft pipe) of 2. As the stiffness ratio (the hard pipe/the soft pipe) increases beyond 26, the hard pipe may be regarded as a rigid pipe. The probability of parametric resonance occurrence will be smallest if the soft–hard combination pipe is supported in a clamped–pinned way. For certain application cases, the safety design length of the two pipes with different materials can be determined through numerical calculation.

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