Abstract
This research aims to calculate the first three natural frequencies and critical velocity of a fluid-conveying pipe are obtained with numerical approach with standard finite element method and this by discretizing the structure wall and internal flow, starting from beam type with two degrees of freedom per node. The determination is done to the vibrational equation from the fluid-structure coupling using Lagrange energy principle. Parameters frequencies are calculated by using a program developed on MATLAB. The advantage of MATLAB language by using standard functions is to present the first Eigen-modes of the system aspect interaction fluid-structure for different physic and geometric parameters in complex planes. The results are converged and compared with those predicted by semi-analytic method. Numerical results show the effect of mass ratio, length and elastic foundation on stability region and static instability and static instability range.
Highlights
The investigation of free vibration and the stability of pipes carrying fluid have attracted the attention of many researchers in the last few periods
The focus in their paper was on instability of infinitely long pipes carrying fluid, by using wave propagation approach, wherein results are interpreted in terms of static instability neutrality as analytic criteria for boundary condition: Pinned-pinned and clampedclamped and dynamic neutrality for clamped-free pipe (Doaré and de Langre, 2006)
In studying and analyzing the concept of instability, the fundamental natural frequency of a pipe decreases with increasing fluid velocity
Summary
The investigation of free vibration and the stability of pipes carrying fluid have attracted the attention of many researchers in the last few periods. Païdoussis and Besancon (1981; Païdoussis, 1981; Païdoussis and Curling, 1985) is the most famous researcher on the topic of mating and thanks to his research, the linear and non-linear equation of the pipes motion was obtained under the influence of many factors (Païdoussis and Moon, 1988; Païdoussis et al, 2007; Païdoussis and Li, 1993) Later on, he published two books (Païdoussis, 2014; 2016) on fluid–structure interactions and the stability of pipes conveying fluid with different parameters. Doaré after him in references (Doaré and de Langre, 2002a; 2002b), he touched better on the issue of static instability and dynamic instability In his studies, he presented analytical models by calculating the critical velocities of fluid. Mohsen and al. studied in the experimental approach based on estimating the critical velocities from the measurement
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