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.

Parametric Resonances of a Cantilevered Pipe Conveying Fluid: A Nonlinear Analysis

1995 ◽  
Author(s):  
C. Semler ◽  
M. P. Païdoussis
Keyword(s):  
Flow Velocity ◽  
Standard Form ◽  
Harmonic Component ◽  
Harmonic Balance Method ◽  
Pipe Conveying Fluid ◽  
Mean Flow ◽  
Incremental Harmonic Balance Method ◽  
Inertial Terms ◽  
The Stability ◽  
Conveying Fluid

Abstract This paper deals with the nonlinear dynamics and the stability of cantilevered pipes conveying fluid, where the fluid has a harmonic component of flow velocity, assumed to be small, superposed on a constant mean value. The mean flow velocity is near the critical value for which the pipe becomes unstable by flutter through a Hopf bifurcation. The partial differential equation is transformed into a set of ordinary differential equations (ODEs) using the Galerkin method. The equations of motion contain nonlinear inertial terms, and hence cannot be put into standard form for numerical integration. Various approaches are adopted to tackle the problem: (a) a perturbation method via which the nonlinear inertial terms are removed by finding an equivalent term using the linear equation; the system is then put into first-order form and integrated using a Runge-Kutta scheme; (b) a finite difference method based on Houbolt’s scheme, which leads to a set of nonlinear algebraic equations that is solved with a Newton-Raphson approach; (c) the stability boundaries are obtained using an incremental harmonic balance method as proposed by S.L. Lau. Using the three methods, the dynamics of the pipe conveying fluid is investigated in detail. For example, the effects of (i) the forcing frequency, (ii) the perturbation amplitude, and (iii) the flow velocity are considered. Particular attention is paid to the effects of the nonlinear terms. These results are compared with experiments undertaken in our laboratory, utilizing elastomer pipes conveying water. The pulsating component of the flow is generated by a plunger pump, and the motions are monitored by a noncontacting optical follower system. It is shown, both numerically and experimentally, that periodic and quasiperiodic oscillations can exist, depending on the parameters.

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.

Parametric and Combination Resonances of a Pipe Conveying Pulsating Fluid

1975 ◽  
Vol 42 (4) ◽  
pp. 780-784 ◽  
Author(s):  
M. P. Paidoussis ◽  
C. Sundararajan
Keyword(s):  
Flow Velocity ◽  
Parametric Resonance ◽  
Mean Value ◽  
Pipe Conveying Fluid ◽  
Combination Resonance ◽  
Load Combination ◽  
Parametric Resonances ◽  
The Difference ◽  
Pulsating Fluid ◽  
Conveying Fluid

In this paper we consider the dynamics of a pipe conveying fluid, when the flow velocity is harmonically perturbed about a mean value. Two methods of analysis are presented; Bolotin’s method, which can only give the boundaries of regions of parametric resonance, and a numerical Floquet analysis, which gives also the boundaries of combination resonance. A number of calculations for cantilevered pipes show that, generally, combination resonance is less important than parametric resonance, except for flow velocities near the critical (where the system loses stability in steady flow); parametric resonances are selectively associated with only some of the modes of the system, and combination resonances involve only the difference of the eigenfrequencies. For pipes clamped at both ends the behavior of the system is similar to that of a column subjected to a pulsating load; combination resonances in this case involve the sum of the eigenfrequencies.

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.

scholarly journals Investigation of approximate mode shape and transition velocity of pipe conveying fluid in failure analysis

2022 ◽  
Vol 14 (1) ◽  
pp. 168781402110724
Author(s):  
Wasiu Adeyemi Oke ◽  
Oluseyi Afolabi Adeyemi ◽  
Ayodeji Olalekan Salau
Keyword(s):  
Failure Analysis ◽  
Mode Shape ◽  
Dynamic Responses ◽  
Mode Shapes ◽  
Pipe Conveying Fluid ◽  
Transition Velocity ◽  
Modal Characteristics ◽  
Pipes Conveying Fluid ◽  
Composite Pipes ◽  
Conveying Fluid

Structures dynamic characteristics and their responses can change due to variations in system parameters. With modal characteristics of the structures, their dynamic responses can be identified. Mode shape remains vital in dynamic analysis of the structures. It can be utilized in failure analysis, and the dynamic interaction between structures and their supports to circumvent abrupt failure. Conversely, unlike empty pipes, the mode shapes for pipes conveying fluid are tough to obtain due to the intricacy of the eigenvectors. Unfortunately, fluid pipes can be found in practice in various engineering applications. Thus, due to their global functions, their dynamic and failure analyses are necessary for monitoring their reliability to avert catastrophic failures. In this work, three techniques for obtaining approximate mode shapes (AMSs) of composite pipes conveying fluid, their transition velocity and relevance in failure analysis were investigated. Hamilton’s principle was employed to model the pipe and discretized using the wavelet-based finite element method. The complex modal characteristics of the composite pipe conveying fluid were obtained by solving the generalized eigenvalue problem and the mode shapes needed for failure analysis were computed. The proposed methods were validated, applied to failure analysis, and some vital results were presented to highlight their effectiveness.

Study on the Influence of Gravity Factor on Parametric Resonance of Pipe Conveying Fluid

2013 ◽  
Vol 300-301 ◽  
pp. 1235-1238
Author(s):  
Bing Chen ◽  
Ming Le Deng ◽  
Zhong Jun Yin
Keyword(s):  
Flow Velocity ◽  
Parametric Resonance ◽  
Resonance Region ◽  
Critical Conditions ◽  
Pipe Conveying Fluid ◽  
First Order ◽  
Comparison Results ◽  
Pipes Conveying Fluid ◽  
The One ◽  
Conveying Fluid

The averaging method has been applied to calculate the critical conditions of parametric resonance instability of the first order mode shape of clamped-clamped and pinned-pinned pipes conveying fluid. The influence of gravity factor on parametric resonance of pipe conveying fluid, with different supporting forms and different flow velocity, has been studied based on the comparison results of gravity factor being considered and neglected. It is concluded that gravity factor has a greater influence on parametric resonance region of pinned-pinned pipe than the one of clamped-clamped pipe, and, at a higher flow velocity, gravity factor is more influential to both pinned-pinned pipe and clamped- clamped one.

Pipes Supported at Both Ends Cannot Flutter

1978 ◽  
Vol 45 (3) ◽  
pp. 619-622 ◽  
Author(s):  
P. J. Holmes
Keyword(s):  
Global Stability ◽  
Pipe Conveying Fluid ◽  
Major Conclusion ◽  
Local And Global Stability ◽  
Simply Supported ◽  
First Order ◽  
Numerical Studies ◽  
Structural Nonlinearities ◽  
Conveying Fluid

We use a development of Liapunov’s second method to study the local and global stability of the equilibrium positions adopted by a pipe conveying fluid. The pipe is simply supported at both ends and the analysis includes first-order (structural) nonlinearities. The major conclusion is that, contrary to the suggestions of linear analyses and of recent nonlinear numerical studies, sustained flutter motions are impossible in the case of the equation studied here.

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