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.

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.

Nonlinear Analysis of L-shaped Pipe Conveying Fluid with the Aid of Absolute Nodal Coordinate Formulation

2021 ◽  
Author(s):  
K. Zhou ◽  
H.R. Yi ◽  
Huliang Dai ◽  
H Yan ◽  
Z.L. Guo ◽  
...  
Keyword(s):  
Theoretical Model ◽  
Flow Velocity ◽  
Absolute Nodal Coordinate Formulation ◽  
Strong Relationship ◽  
Excitation Amplitude ◽  
Pipe Conveying Fluid ◽  
Base Excitation ◽  
Absolute Nodal Coordinate ◽  
Nonlinear Behaviors ◽  
Conveying Fluid

Abstract By adopting the absolute nodal coordinate formulation, a novel and general nonlinear theoretical model, which can be applied to solve the dynamics of combined straight-curved fluid-conveying pipes with arbitrary initially configurations and any boundary conditions, is developed in the current study. Based on this established model, the nonlinear behaviors of the cantilevered L-shaped pipe conveying fluid with and without base excitations are systematically investigated. Before starting the research, the developed theoretical model is verified by performing three validation examples. Then, with the aid of this model, the static deformations, linear stability, and nonlinear self-excited vibrations of the L-shaped pipe without the base excitation are determined. It is found that the cantilevered L-shaped pipe suffers from the static deformations when the flow velocity is subcritical, and will undergo the limit-cycle motions as the flow velocity exceeds the critical value. Subsequently, the nonlinear forced vibrations of the pipe with a base excitation are explored. It is indicated that the period-n, quasi-periodic and chaotic responses can be detected for the L-shaped pipe, which has a strong relationship with the flow velocity, excitation amplitude and frequency.

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.

Stabilization of a flexible pipe conveying fluid with an active boundary control method

2020 ◽  
Vol 26 (19-20) ◽  
pp. 1824-1834
Author(s):  
Beiming Yu ◽  
Hiroshi Yabuno ◽  
Kiyotaka Yamashita
Keyword(s):  
Flow Velocity ◽  
Control Method ◽  
Bending Moment ◽  
The Self ◽  
Pipe Conveying Fluid ◽  
Stabilization Method ◽  
Critical Flow Velocity ◽  
Complex Eigenvalues ◽  
Excited Oscillation ◽  
Conveying Fluid

A method of stabilizing the self-excited oscillation of a cantilevered pipe conveying fluid because of non–self-adjointness is proposed theoretically and experimentally. Complex eigenvalues denoting the natural frequency and damping of the system vary with an increase in the flow velocity. When the flow velocity exceeds a critical value, the flow-generated damping becomes negative and the pipe is dynamically destabilized. The complex eigenvalues with respect to flow velocity are affected by boundary conditions. We, thus, propose a stabilization control actuating the boundary condition. The stabilization method is carried out by applying a bending moment proportional to the bottom displacement of the pipe. The effect of the proposed control method is shown by investigating the stability for the three lowest modes of the system depending on the feedback gain. It is theoretically clarified that the critical flow velocity is increased by the proposed control method. Furthermore, experiments are performed using a fluid conveying pipe with two piezoactuators at the downstream end. The piezoactuators apply a bending moment at the downstream end of the pipe according to the theoretically proposed method. Experimental results verify that the proposed stabilization method suppresses the self-excited oscillation.

Dynamic Behavior of Continuous Cantilevered Pipes Conveying Fluid Near Critical Velocities

1981 ◽  
Vol 48 (4) ◽  
pp. 943-947 ◽  
Author(s):  
J. Rousselet ◽  
G. Herrmann
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Flow Velocity ◽  
Averaging Method ◽  
Nonlinear Partial Differential Equations ◽  
Plane Motion ◽  
Pipe Conveying Fluid ◽  
Pipes Conveying Fluid ◽  
Critical Velocities ◽  
Conveying Fluid

The plane motion of a cantilevered pipe conveying fluid is examined when the flow velocity is in the neighborhood of that generating flutter. In contrast to previous studies, the flow velocity is not prescribed as a constant, but is determined from the laws of motion. We are thus led to a system of two nonlinear partial differential equations which are coupled through the nonlinear terms. The solution is found by the use of the Krylov-Bogoliubov averaging method and the results are discussed indicating the effect of nonlinearities.

scholarly journals Dynamical response of a rotating cantilever pipe conveying fluid based on the absolute nodal coordinate formulation

2021 ◽  
Vol 37 ◽  
pp. 359-372
Author(s):  
Yunfeng Li ◽  
Yundong Li ◽  
Huabin Wen ◽  
Wenbo Ning
Keyword(s):  
Flow Velocity ◽  
Absolute Nodal Coordinate Formulation ◽  
Static Deformation ◽  
Dynamical Response ◽  
Pipe Conveying Fluid ◽  
Absolute Nodal Coordinate ◽  
Variation Of Parameters ◽  
Angular Velocities ◽  
The Absolute ◽  
Conveying Fluid

Abstract A dynamical model of a rotating cantilever pipe conveying fluid is derived based on the absolute nodal coordinate formulation. The free vibration and dynamical response of the system are investigated in this paper. Based on the absolute nodal coordinate method and the extended Lagrangian equation proposed by Irschik for the nonmaterial system, the motion equation of the rotating flexible cantilever pipe conveying fluid is built. The influence of the rotational angular velocity and flow velocity on the natural frequency of the system is analyzed. The critical nondimensional circular frequency of in-plane vibration and critical nondimensional flow velocity are investigated. The static deformation is shown under different flow velocities and angular velocities. The nonlinear transient analyses of a rotating flexible cantilever pipe are completed with the variation of parameters. During the rotation, the Coriolis force of fluid acting on the pipe has a great effect on the static deformation.

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.

Reliability of a Single β-Thromboglobulin Measurement in a Diabetic Population : Importance of PGE1 in Anticoagulant Mixture

1987 ◽  
Vol 57 (02) ◽  
pp. 201-204 ◽  
Author(s):  
P Y Scarabin ◽  
L Strain ◽  
C A Ludlam ◽  
J Jones ◽  
E M Kohner
Keyword(s):  
In Vitro Release ◽  
Mean Value ◽  
Reliable Estimate ◽  
Diabetic Patients ◽  
Single Measurement ◽  
Diabetic Population ◽  
The Difference ◽  
Vitro Release

SummaryDuring the collection of samples for plasma β-thromboglobulin (β-TG) determination, it is well established that artificially high values can be observed due to in-vitro release. To estimate the reliability of a single β-TG measurement, blood samples were collected simultaneously from both arms on two separate occasions in 56 diabetic patients selected for a clinical trial. From each arm, blood was taken into two tubes containing an anticoagulant mixture with (tube A) and without (tube B) PGE!. The overall mean value of B-TG in tube B was 1.14 times higher than in tube A (p <0.01). The markedly large between-arms variation accounted for the most part of within-subject variation in both tubes and was significantly greater in tube B than in tube A. Based on the difference between B-TG values from both arms, the number of subjects with artifically high B-TG values was significantly higher in tube B than in tube A on each occasion (overall rate: 28% and 14% respectively). Estimate of between-occasions variation showed that B-TG levels were relatively stable for each subject between two occasions in each tube. It is concluded that the use of PGEi decreases falsely high B-TG levels, but a single measurement of B-TG does not provide a reliable estimate of the true B-TG value in vivo.

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