Does a Partial Elastic Foundation Increase the Flutter Velocity of a Pipe Conveying Fluid?

2000 ◽  
Vol 68 (2) ◽  
pp. 206-212 ◽  
Author(s):  
I. Elishakoff ◽  
N. Impollonia
Keyword(s):  
Critical Velocity ◽  
Entire Length ◽  
Velocity Versus ◽  
Winkler Foundation ◽  
Strengthening Effect ◽  
Pipe Conveying Fluid ◽  
Follower Forces ◽  
The Stability ◽  
Realistic Structure ◽  
Conveying Fluid

The effect of the elastic Winkler and rotatory foundations on the stability of a pipe conveying fluid is investigated in this paper. Both elastic foundations are partially attached to the pipe. It turns out that the single foundation, either translational or rotatory, which is attached to the pipe along its entire length, increases the critical velocity. Such an intuitively anticipated strengthening effect is surprisingly missing for the elastic column on Winkler foundation subjected to the so-called statically applied follower forces. Yet, partial foundation for the pipe conveying fluid is associated with a nonmonotonous dependence of the critical velocity versus the attachment ratio defined as the length of the partial foundation over the entire length of the pipe. It is concluded that such a paradoxical nonmonotonicity is shared by both the realistic structure (pipe conveying fluid) and in the “imagined system,” to use the terminology of Herrmann pertaining to the column under to follower forces.

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.

605 An Experimental Study on the Stability and the Optimal Design of a Combined Pipe Conveying Fluid

2001 ◽  
Vol 2001 (0) ◽  
pp. 175-176
Author(s):  
Hitoshi DOKI ◽  
Kazuhiko HIRAMOTO ◽  
Tomomichi MIYAZAKI ◽  
Motohiro MISHIMA
Keyword(s):  
Experimental Study ◽  
Optimal Design ◽  
Pipe Conveying Fluid ◽  
The Stability ◽  
Conveying Fluid

Dynamic behaviors of multi-span viscoelastic functionally graded material pipe conveying fluid

2016 ◽  
Vol 231 (17) ◽  
pp. 3181-3192 ◽  
Author(s):  
Jiaquan Deng ◽  
Yongshou Liu ◽  
Zijun Zhang ◽  
Wei Liu
Keyword(s):  
Functionally Graded Material ◽  
Volume Fraction ◽  
Fluid Velocity ◽  
Functionally Graded ◽  
Piping System ◽  
Pipe Conveying Fluid ◽  
Dynamic Behaviors ◽  
Graded Material ◽  
The Stability ◽  
Conveying Fluid

In this paper, the dynamic behaviors of a multi-span viscoelastic functionally graded material pipe conveying fluid are investigated by dynamic stiffness method. The material properties of the functionally graded material pipe are considered as graded distribution along the thickness direction according to a power-law. Several numerical examples are performed to study the effects of volume fraction exponent, fluid velocity, internal pressure, and internal damping on the stability and frequency response of the fluid-conveying functionally graded material pipe. It’s found that the viscoelastic functionally graded material pipe exhibits some special dynamic behaviors and it could increase the stability significantly when compared with the aluminum and steel pipes. The numerical results also demonstrate that by the introduction of the functionally graded material, the stiffness of the piping system could be modulated easily by designing the volume fraction function. Therefore, if the dominant frequency contents of the external loads are known, a preferable design of the functionally graded material pipe to reduce the vibration is possible.

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.

EFFECTS OF TIP MASS ON STABILITY OF ROTATING CANTILEVER PIPE CONVEYING FLUID WITH CRACK

2010 ◽  
Vol 24 (15n16) ◽  
pp. 2609-2614 ◽  
Author(s):  
IN SOO SON ◽  
HAN IK YOON ◽  
SANG PIL LEE ◽  
DONG JIN KIM
Keyword(s):  
Angular Velocity ◽  
Equations Of Motion ◽  
Pipe Conveying Fluid ◽  
Mass Ratio ◽  
Critical Flow Velocity ◽  
Pipe System ◽  
Stability Maps ◽  
The Stability ◽  
Tip Mass ◽  
Conveying Fluid

In this paper, the dynamic stability of a rotating cantilever pipe conveying fluid with a crack and tip mass is investigated by numerical method. That is, the effects of the rotating the rotating angular velocity, the mass ratio, the crack and tip mass on the critical flow velocity for flutter instability of system are studied. The equations of motion of rotating pipe are derived by using the extended Hamilton's principle. The crack section of pipe is represented by a local flexibility matrix connecting two undamaged pipe segments. The crack is assumed to be in the first mode of fracture and always opened during the vibrations. Finally, the stability maps of the cracked rotating pipe system as a rotating angular velocity and mass ratio β are presented.

Sign in / Sign up

Export Citation Format

Share Document