Dynamics and Stability of Pipes Conveying Fluid

1994 ◽  
Vol 116 (1) ◽  
pp. 57-66 ◽  
Author(s):  
C. O. Chang ◽  
K. C. Chen
Keyword(s):  
Equations Of Motion ◽  
Stability Boundary ◽  
Harmonic Component ◽  
Mean Value ◽  
Transverse Motion ◽  
Perturbation Techniques ◽  
Damped System ◽  
Pipes Conveying Fluid ◽  
The Stability ◽  
Conveying Fluid

This paper deals with the dynamics and stability of simply supported pipes conveying fluid, where the fluid has a small harmonic component of flow velocity superposed on a constant mean value. The perturbation techniques and the method of averaging are used to convert the nonautonomous system into an autonomous one and determine the stability boundaries. Post-bifurcation analysis is performed for the parametric points in the resonant regions where the axial force, which is induced by the transverse motion of the pipe due to the fixed-span ends and contributes nonlinearities to the equations of motion, is included. For the undamped system, linear analysis is inconclusive about stability and there does not exist nontrivial solution in the resonant regions. For the damped system, it is found that the original stable system remains stable when the pulsating frequency increases cross the stability boundary and becomes unstable when the pulsating frequency decreases cross the stability boundary.

A Hybrid Ale Formulation for the Investigation of the Stability of Pipes Conveying Fluid and Axially Moving Beams

2022 ◽  
Author(s):  
Michael Pieber ◽  
Konstantina Ntarladima ◽  
Robert Winkler ◽  
Johannes Gerstmayr
Keyword(s):  
Equations Of Motion ◽  
Arbitrary Lagrangian Eulerian ◽  
Multibody Modeling ◽  
Ale Formulation ◽  
Conveyor Belts ◽  
Axially Moving Beams ◽  
Pipes Conveying Fluid ◽  
Axially Moving ◽  
The Stability ◽  
Conveying Fluid

Abstract The present work addresses pipes conveying fluid and axially moving beams undergoing large deformations. A novel two dimensional beam finite element is presented, based on the Absolute Nodal Coordinate Formulation (ANCF) with an extra Eulerian coordinate to describe axial motion. The resulting formulation is well known as Arbitrary Lagrangian Eulerian (ALE) method, which is often used to model axially moving beams and pipes conveying fluid. The proposed approach, which is derived from an extended version of Lagrange's equations of motion, allows for the investigation of the stability of pipes conveying fluid and axially moving beams for a certain axial velocity and stationary state of large deformation. Additionally, a multibody modeling approach allows us to extend the beam formulation for co-moving discrete masses, which represent concentrated masses attached to the beam, e.g., gondolas in ropeway systems, or transported masses in conveyor belts. Within numerical investigations, we show that axially moving beams and a larger number of discrete masses behave similarly as the case of (continuously) distributed mass.

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.

The Dynamic Behavior of Articulated Pipes Conveying Fluid With Periodic Flow Rate

1974 ◽  
Vol 41 (1) ◽  
pp. 55-62 ◽  
Author(s):  
M. P. Bohn ◽  
G. Herrmann
Keyword(s):  
Flow Rate ◽  
Mean Value ◽  
Plane Motion ◽  
Periodic Disturbances ◽  
Rate Oscillation ◽  
Driven System ◽  
Pipes Conveying Fluid ◽  
Minimum Amplitude ◽  
Small Periodic ◽  
Conveying Fluid

The plane motion of two rigid, straight articulated pipes conveying fluid is examined. In contrast to previous work, the flow rate is not taken as constant, but is allowed to have small periodic oscillations about a mean value, as would be expected in a pump-driven system. It is shown that in the presence of such disturbances, both parametric and combination resonances are possible. When the system can also admit loss of stabilty by static buckling or by flutter, it is found that the presence of small periodic disturbances constitutes a destabilizing effect. Floquet theory and converging infinite determinant expansions are used to illustrate a basic difference between systems which lose stability by divergence and those that lose stability by flutter. An algebraic criterion is obtained for the minimum amplitude of flow rate oscillation required for the system to be affected by the presence of small disturbances.

Influence of Nonlinearities on the Behavior of Parametrically Excited Articulated Pipes Conveying Fluid

1978 ◽  
Vol 5 (1) ◽  
pp. 31-38 ◽  
Author(s):  
J. Rousselet ◽  
G. Herrmann
Keyword(s):  
Fluid Flow ◽  
Stability Analysis ◽  
Dynamic Systems ◽  
Linear Formulation ◽  
Fluctuating Pressure ◽  
The Past ◽  
Pipes Conveying Fluid ◽  
Critical Velocities ◽  
The Stability ◽  
Conveying Fluid

This paper presents the analysis of a system of articulated pipes hanging vertically under the influence of gravity. The liquid, driven by a slightly fluctuating pressure, circulates through the pipes. Similar systems have been analysed in the past by numerous authors but a common feature of their work is that the behavior of the fluid flow is prescribed, rather than left to be determined by the laws of motion. This leads to a linear formulation of the problem which can not predict the behavior of the system for finite amplitudes of motion. A circumstance in which this behavior is important arises in the stability analysis of the system in the neighbourhood of critical velocities, that is, flow velocities at which the system starts to flutter. Hence, the purpose of the present study was to investigate in greater detail the region close to critical velocities in order to find by how much these critical velocities would be affected by the amplitudes of motion. This led to a set of three coupled-nonlinear equations, one of which represents the motion of the fluid. In the mathematical development, use is made of a scheme which permits the uncoupling of the modes of motion of damped nonconservative dynamic systems. Results are presented showing the importance of the nonlinearities considered.

On the Dynamic Stability of Self-Aligning Journal Gas Bearings

1977 ◽  
Vol 99 (4) ◽  
pp. 434-440 ◽  
Author(s):  
M. J. Cohen
Keyword(s):  
Dynamic Stability ◽  
Journal Bearing ◽  
Equations Of Motion ◽  
Stability Boundary ◽  
Initial Condition ◽  
Small Motion ◽  
Gas Bearings ◽  
Loading Case ◽  
The Stability ◽  
Small Disturbances

The report presents an investigation of the dynamic stability behaviour of self-aligning journal gas bearings when subjected to arbitrary small disturbances from an initial condition of operational equilibrium. The method is based on an approach similar to the nonlinear-ph solution of the author for the quasi-static loading case but the equations of motion of the journal are the linearized forms for small motion in the two degrees (translational) of freedom of the journal center. The stability domains for the infinite journal bearing are presented for the whole of the eccentricity (ε) and rotational speed (Λ) ranges for any given bearing geometry, in the shape of stability boundaries in that domain. It is shown that a given bearing will be stable within a corridor in the (ε, Λ) parametral domain having as its lower bound the so called “half-speed” whirl stability boundary and as its upper bound another whirling instability at a higher characteristic (relative) frequency, the instability occurs generally at the higher eccentricities and lower rotational speeds.

scholarly journals Influence of Dry Friction on the Dynamics of Cantilevered Pipes Conveying Fluid

2022 ◽  
Vol 12 (2) ◽  
pp. 724
Author(s):  
Zilong Guo ◽  
Qiao Ni ◽  
Lin Wang ◽  
Kun Zhou ◽  
Xiangkai Meng
Keyword(s):  
Flow Velocity ◽  
Friction Force ◽  
Dry Friction ◽  
Critical Flow Velocity ◽  
Pipe System ◽  
Pipes Conveying Fluid ◽  
Cantilevered Pipe ◽  
The Stability ◽  
Friction Parameters ◽  
Conveying Fluid

A cantilevered pipe conveying fluid can lose stability via flutter when the flow velocity becomes sufficiently high. In this paper, a dry friction restraint is introduced for the first time, to evaluate the possibility of improving the stability of cantilevered pipes conveying fluid. First, a dynamical model of the cantilevered pipe system with dry friction is established based on the generalized Hamilton’s principle. Then the Galerkin method is utilized to discretize the model of the pipe and to obtain the nonlinear dynamic responses of the pipe. Finally, by changing the values of the friction force and the installation position of the dry friction restraint, the effect of dry friction parameters on the flutter instability of the pipe is evaluated. The results show that the critical flow velocity of the pipe increases with the increment of the friction force. Installing a dry friction restraint near the middle of the pipe can significantly improve the stability of the pipe system. The vibration of the pipe can also be suppressed to some extent by setting reasonable dry friction parameters.

scholarly journals Stability Analysis of Fluid-Conveying Beams using Artificial Intelligence

2018 ◽  
Vol 3 (1) ◽  
Author(s):  
Theddeus T Akano ◽  
Olumuyiwa S Asaolu
Keyword(s):  
Artificial Intelligence ◽  
Fuzzy Inference ◽  
Fuzzy Model ◽  
Inference System ◽  
Fluid Field ◽  
Neuro Fuzzy ◽  
Pipes Conveying Fluid ◽  
The Stability ◽  
Stability Results ◽  
Conveying Fluid

This paper employs artificial intelligence in predicting the stability of pipes conveying fluid. Field data was collected for different pipe structures and usage. Adaptive Neuro-Fuzzy Inference System (ANFIS) model is implemented to predict the stability of the pipe using the fundamental natural frequency at different flow velocities as the index of stability. Results reveal that the neuro-fuzzy model compares relatively well with the conventional finite element method. It was also established that a pipe conveying fluid is most stable when the pipe is clamped at both ends but least stable when it is a cantilever.

Nonlinear Free Vibration of Spinning Viscoelastic Pipes Conveying Fluid

2018 ◽  
Vol 10 (07) ◽  
pp. 1850076 ◽  
Author(s):  
Feng Liang ◽  
Xiao-Dong Yang ◽  
Wei Zhang ◽  
Ying-Jing Qian
Keyword(s):  
Oil And Gas ◽  
Multiple Scales ◽  
Equations Of Motion ◽  
Drill String ◽  
Mode Shapes ◽  
Flowing Fluid ◽  
Nonlinear Dynamical ◽  
Pipes Conveying Fluid ◽  
Spinning Speed ◽  
Conveying Fluid

Drill strings are one of the most significant rotor components employed in oil and gas exploitation. In this paper, an improved dynamical model of drill-string-like pipes conveying fluid is developed by taking into account the axial spin, fluid–structure interaction (FSI), damping as well as curvature and inertia nonlinearities. The partial differential equations of motion are derived by two sequential Euler angles and the Hamilton principle and then directly handled by the multiple scales method. The nonlinear amplitudes, frequencies and whirling mode shapes are all investigated towards various system parameters to display the nonlinear dynamical characteristics of such a special rotor system coupled with FSI. It is revealed that the nonlinear amplitudes and frequencies are explicitly dependent on the spinning speed, while the flowing fluid mainly contributes to the linear frequencies, and consequently influences the nonlinear amplitudes and frequencies. The FSI effect and axial spin can both improve the forward procession mode and suppress the backward one, while both procession modes will be suppressed by the viscoelastic damping. The pipe will ultimately present a forward as well as decayed whirling motion for the fundamental mode.

Dynamic Stability of Periodic Pipes Conveying Fluid

2013 ◽  
Vol 81 (1) ◽  
Author(s):  
Dianlong Yu ◽  
Michael P. Païdoussis ◽  
Huijie Shen ◽  
Lin Wang
Keyword(s):  
Material Properties ◽  
Unit Length ◽  
Mass Parameter ◽  
High Accuracy ◽  
Pipe Conveying Fluid ◽  
Good Convergence ◽  
System Parameters ◽  
Pipes Conveying Fluid ◽  
The Stability ◽  
Conveying Fluid

In this paper, the stability of a periodic cantilevered pipe conveying fluid is studied theoretically by means of a novel transfer matrix method. This method is first validated by comparing the results to those available in the literature for a uniform pipe, showing that it is capable of high accuracy and displaying good convergence characteristics. Then, the stability of periodic pipes is investigated, with geometric, material-properties periodicity, and a combination of the two, showing that a considerable stabilizing effect may be achieved over different ranges of the mass parameter β (β=mf/(mf+mp), where mf and mp are the fluid and pipe masses per unit length). The effect of other different system parameters is also probed.

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