The dynamic stability of a pipe conveying a pulsatile flow

Ahn

et al. 2006

The dynamic behavior of the cylindrical shell with uniform flow is formulated by the finite element method. The dynamics of the shell is based on Donnell's theory and the fluid in cylindrical shell is considered satisfying the Helmholtz equation. The effective thickness of fluid is calculated according to the circumferential modes and the frequencies. An estimation of the FRF (frequency response function) of the shell with taking into consideration of the coupled effects of the internal fluid is presented. These results are compared with the results considering fluid satisfying Laplace equation. The influence of fluid velocity on the FRF is also discussed.

Section: Introductionmentioning

confidence: 99%

Finite Element Vibration Analysis of Cylindrical Shells Conveying Fluid with Considering Acoustic-Structure Interactions

Ahn

et al. 2006

“…Ginsberg (1) derived the equation of motion of a pipe for any end condition and investigated the stability. Paidoussis (2), (3) developed numerical methods to check whether a point lies in the stable or the unstable region by calculating the determinant of a large matrix for every point in the parametric space.…”

Section: Introductionmentioning

confidence: 99%

“…This method was based on the Floquet theory (6) , which extended the stability boundaries of Bolotin (7) method. These studies (1), (3), (5) carried out the stability analysis by using assumed mode method, which could be only applied when the modes of a pipe were known. Seo (9) presented the finite element model to overcome the demerits of assumed mode method.…”

Section: Introductionmentioning

confidence: 99%

“…Seo (9) presented the finite element model to overcome the demerits of assumed mode method. But, these studies (1), (3), (5), (8) assumed that the fluid in a pipe had only single frequency pulsation. However, in most real cases, the fluid in a pipe pulsates periodically, which means that the pulsations have several harmonics of fundamental period.…”

Section: Introductionmentioning

confidence: 99%

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Stability Analysis of a Pipe Conveying Periodically Pulsating Fluid Using Finite Element Method

et al. 2006

It is well known that the constant velocity of the fluid in a pipe which makes the lowest natural frequency zero is called critical velocity. The pipe becomes unstable when the fluid in a pipe is faster than the critical velocity. If the velocity of the fluid in a pipe varies with time, however, the instability of a pipe will occur even though the mean velocity of the fluid is below the critical velocity. In this paper, a new method for the stability analysis of a pipe conveying fluid which pulsates periodically is presented. The finite element model is formulated to solve the governing equation numerically. The coupled effects of several harmonic components in the velocity of fluid to a pipe is discussed. A new unstable region is shown in this paper which will not appear in the stability analysis of single pulsating frequency. The results of the stability analysis presented in this paper are verified by the time domain anlysis.

“…This method was based on the Floquet theory (6) , based on Bolotin (7) , which extended the stability boundaries. These previous studies (1), (3), (5) were based on the assumed mode method. But it might be difficult to assume the mode of a pipe with a complicated shape.…”

Section: Introductionmentioning

confidence: 99%

Finite Element Analysis of Forced Vibration for a Pipe Conveying Harmonically Pulsating Fluid

et al. 2005

It is well known that the natural frequencies of a pipe become lower as uniform internal fluid velocity increases. The pipe becomes unstable if the fluid is faster than the critical velocity. But in the case of a pipe conveying harmonically pulsating fluid, resonances will occur even though the mean velocity of the fluid is below the critical velocity. Therefore, for improved analysis, the effects of pulsating fluid in the pipe should also be taken into consideration. In this study, a finite element formulation for the pipe was carried out while taking into consideration the effects of the fluid pulsating harmonically in the pipe. The damping and stiffness matrices in the finite element equation vary with time. A stability analysis based on the Bolotin method was carried out. And, a method to directly estimate the forced response of the pipe that does not need to solve a time data from time-variant system is presented. Several numerical examples are given in this paper that validate of this method.