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

This  paper  deals  with  the  analytical  modelisation and  the  numerical  simulation  of  fluid  structure  interaction (FSI)  phenomena  of  pipeline.  The  equations  of  motions and  equilibrium  are  coupled  together  taking  into  account the  influence  of  the  fluid  flow  inside  the  pipe.  The  fluid circulating  in  the  pipe  has  the  flexional  motion  as  that  of structure.  The  analytical  model  is  based  on  the  Newtonian approach.  The  practicability  of  the  calculation  model  and the  effects  of  fluid-structure  interaction  are  illustrated  by calculations  for  some  simple  systems,  for  pipe  with boundary  condition  pinned-pinned.  Independently  of  the analytical  method,  a  numerical  modal  analysis  is  realized in  the  fluid  structure  configuration.  This  configuration  has been  simulated  by  coupling  the  two  commercial  solvers: Fluent  code  of  fluid  mechanical  (CFD,  Computational Fluid  Dynamics),  and  ANSYS  classical  code  of  structure mechanical  (CSD,  Computational  structure  Dynamics)  for pipes  with  different  boundary  conditions:  pinned-pinned, clamped-pinned  and  clamped-clamped.  We  describe  the technique  used  to  solve  the  equations  associated  in  the determination  of  natural  frequencies.  For  this,  we  use  code ANSYS  Workbench  where  the  equations  are  discritized with  finite  element  method.  The  results  obtained numerically  are  similar  to  those  obtained  by  the  analytical approach.DOI: http://dx.doi.org/10.5755/j01.mech.22.6.13189

https://mechanika.ktu.lt/index.php/Mech/article/download/13189/8590

One-way fluid structure interaction of pipe under flow with different boundary conditions

General analytical solution for vibrations of pipes with arbitrary discontinuities and generalized boundary condition on Pasternak foundation

The problem of stability of fluid-conveying carbon nanotubes embedded in an elastic medium is investigated in this paper. A nonlocal continuum mechanics formulation, which takes the small length scale effects into consideration, is utilized to derive the governing fourth-order partial differential equations. The Fourier series method is used for the case of the pinned–pinned boundary condition of the tube. The Galerkin technique is utilized to find a solution of the governing equation for the case of the clamped–clamped boundary. Closed-form expressions for the critical flow velocity are obtained for different values of the Winkler and Pasternak foundation stiffness parameters. Moreover, new and interesting results are also reported for varying values of the nonlocal length parameter. It is observed that the nonlocal length parameter along with the Winkler and Pasternak foundation stiffness parameters exert considerable effects on the critical velocities of the fluid flow in nanotubes.

Critical velocities in fluid-conveying single-walled carbon nanotubes embedded in an elastic 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.

Kameswara Rao Chellapilla

Papers

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