Natural frequency analysis of fluid conveying pipeline with different boundary conditions

This paper deals with nonlocal divergence and flutter instability analysis of carbon nanotubes (CNTs) conveying fluid embedded in an elastic foundation under magnetic field. Nonlocal constitutive equations of Eringen and Euler–Bernoulli beam theory are used in the formulations. Also, the foundation is described by the Winkler and Pasternak models. The governing equation of motion and boundary conditions are derived using extended Hamilton’s variational principle. The extended Galerkin’s approach is adopted to reduce the partial differential equation governing the dynamics of the CNTs to a system of coupled ordinary differential equations. In the present study, four different boundary conditions are considered, namely the pined–pined (P–P), clamped–pined (C–P), clamped–clamped (C–C) and clamped–free (C–F). A detailed parametric study is conducted to elucidate the effects of the nonlocal effect, longitudinal magnetic field, elastic Winkler and Pasternak foundations and geometrically boundary conditions on the instability characteristic of CNTs. It was observed that the only instability type for the investigated CNT with clamped–free boundary condition (cantilever) is flutter, while CNT conveying fluid with both ends supported loses its stability by divergence first and then by flutter with increase in fluid velocity. It was also found that the magnetic field and the Winkler and Pasternak foundations increase the stiffness of the system. Therefore, flutter instability region is enlarged significantly due to the existence of springs, shear foundations and magnetic field. Also, results show that the nonlocal parameter has a prominent effect on the stability behavior of CNTs, in which increasing nonlocal parameter results in the decrease in stability region. Furthermore, it was shown that the stability behavior of CNT is strongly affected by different boundary conditions. Finally, the validity of the present analysis is confirmed by comparing the results with those obtained from the literature.

Nonlocal divergence and flutter instability analysis of embedded fluid-conveying carbon nanotube under magnetic field

Analytical predictions for vibration phase shifts along fluid-conveying pipes due to Coriolis forces and imperfections

Free vibration and stability analysis of a multi-span pipe conveying fluid using exact and variational iteration methods combined with transfer matrix method

In this study, we investigate the effect of a nonuniform Winkler-type elastic foundation on the stability of pipes conveying fluid fixed at the upstream end only. A stability analysis of transverse motion aims at determining the flutter velocity as a function of the governing control parameters such as fluid mass over the pipe mass ratio, or foundation stiffness. The global stability of the system is analyzed applying an ad-hoc developed finite-element formulation that leads to a discrete state-space equation of motion. It is shown that for a uniform foundation, an increased stiffness of the Winkler coefficient leads to an increased critical flow speed for any value fluid/pipe mass ratio, while in the case of a nonuniform elastic foundation, the system may present higher or lower critical flow speed depending on the fluid/pipe mass ratio. Special attention is paid to the “&#x1d4c8;” type behavior of the instability curves, as reported in numerous papers.

FEM Formulation for Dynamic Instability of Fluid-Conveying Pipe on Nonuniform Elastic Foundation

https://www.researchgate.net/profile/Hari_Simha/publication/228672490_Vibrations_of_Fluid-Conveying_Pipes_Resting_on_Two-parameter_Foundation/links/02e7e52e1ec4794c12000000.pdf

Critical velocity of fluid-conveying pipes resting on two-parameter foundation

The problem of vibrations of fluid-conveying pipes resting on a two-parameter foundation model such as the Pasternak-Winkler model is studied in this paper. Fluid-conveying pipes with ends that are pinned-pinned, clamped- pinned and clamped-clamped are considered for study. The frequency expression is derived using Fourier series for the pinned-pinned case. Galerkin's technique is used in obtaining the frequency expressions for the clamped-pinned and clamped-clamped boundary conditions. The effects of the transverse and shear parameters related to the Pasternak- Winkler model and the fluid flow velocity parameter on the frequencies of vibration are studied based on the numerical results obtained for various pipe end conditions. From the results obtained, it is observed that the instability caused by the fluid flow velocity is effectively countered by the foundation and the fluid conveying pipe is stabilized by an appropriate choice of the stiffness parameters of the Pasternak-Winkler foundation. A detailed study is made on the influence of Pasternak-Winkler foundation on the frequencies of vibration of fluid conveying pipes and interesting conclusions are drawn from the numerical results presented for pipes with different boundary conditions.

H.S. Simha

Papers

Critical velocity of fluid-conveying pipes resting on two-parameter foundation

Vibrations of Fluid-Conveying Pipes Resting on Two-parameter Foundation