Nonlinear analysis of L-shaped pipe conveying fluid with the aid of absolute nodal coordinate formulation

2021 ◽  
Author(s):  
K. Zhou ◽  
H. R. Yi ◽  
H. L. Dai ◽  
H. Yan ◽  
Z. L. Guo ◽  
...  
Keyword(s):  
Nonlinear Analysis ◽  
Absolute Nodal Coordinate Formulation ◽  
Pipe Conveying Fluid ◽  
Absolute Nodal Coordinate ◽  
Conveying Fluid

Nonlinear Analysis of L-shaped Pipe Conveying Fluid with the Aid of Absolute Nodal Coordinate Formulation

2021 ◽  
Author(s):  
K. Zhou ◽  
H.R. Yi ◽  
Huliang Dai ◽  
H Yan ◽  
Z.L. Guo ◽  
...  
Keyword(s):  
Theoretical Model ◽  
Flow Velocity ◽  
Absolute Nodal Coordinate Formulation ◽  
Strong Relationship ◽  
Excitation Amplitude ◽  
Pipe Conveying Fluid ◽  
Base Excitation ◽  
Absolute Nodal Coordinate ◽  
Nonlinear Behaviors ◽  
Conveying Fluid

Abstract By adopting the absolute nodal coordinate formulation, a novel and general nonlinear theoretical model, which can be applied to solve the dynamics of combined straight-curved fluid-conveying pipes with arbitrary initially configurations and any boundary conditions, is developed in the current study. Based on this established model, the nonlinear behaviors of the cantilevered L-shaped pipe conveying fluid with and without base excitations are systematically investigated. Before starting the research, the developed theoretical model is verified by performing three validation examples. Then, with the aid of this model, the static deformations, linear stability, and nonlinear self-excited vibrations of the L-shaped pipe without the base excitation are determined. It is found that the cantilevered L-shaped pipe suffers from the static deformations when the flow velocity is subcritical, and will undergo the limit-cycle motions as the flow velocity exceeds the critical value. Subsequently, the nonlinear forced vibrations of the pipe with a base excitation are explored. It is indicated that the period-n, quasi-periodic and chaotic responses can be detected for the L-shaped pipe, which has a strong relationship with the flow velocity, excitation amplitude and frequency.

scholarly journals Dynamical response of a rotating cantilever pipe conveying fluid based on the absolute nodal coordinate formulation

2021 ◽  
Vol 37 ◽  
pp. 359-372
Author(s):  
Yunfeng Li ◽  
Yundong Li ◽  
Huabin Wen ◽  
Wenbo Ning
Keyword(s):  
Flow Velocity ◽  
Absolute Nodal Coordinate Formulation ◽  
Static Deformation ◽  
Dynamical Response ◽  
Pipe Conveying Fluid ◽  
Absolute Nodal Coordinate ◽  
Variation Of Parameters ◽  
Angular Velocities ◽  
The Absolute ◽  
Conveying Fluid

Abstract A dynamical model of a rotating cantilever pipe conveying fluid is derived based on the absolute nodal coordinate formulation. The free vibration and dynamical response of the system are investigated in this paper. Based on the absolute nodal coordinate method and the extended Lagrangian equation proposed by Irschik for the nonmaterial system, the motion equation of the rotating flexible cantilever pipe conveying fluid is built. The influence of the rotational angular velocity and flow velocity on the natural frequency of the system is analyzed. The critical nondimensional circular frequency of in-plane vibration and critical nondimensional flow velocity are investigated. The static deformation is shown under different flow velocities and angular velocities. The nonlinear transient analyses of a rotating flexible cantilever pipe are completed with the variation of parameters. During the rotation, the Coriolis force of fluid acting on the pipe has a great effect on the static deformation.

A Large Deformation Finite Element for Pipes Conveying Fluid Based on the Absolute Nodal Coordinate Formulation

2007 ◽  
Author(s):  
Michael Stangl ◽  
Johannes Gerstmayr ◽  
Hans Irschik
Keyword(s):  
Finite Element ◽  
Large Deformation ◽  
Absolute Nodal Coordinate Formulation ◽  
Equations Of Motion ◽  
Directional Derivatives ◽  
Absolute Nodal Coordinate ◽  
Lagrange’S Equations ◽  
The Absolute ◽  
Lagrange's Equations ◽  
Conveying Fluid

A novel pipe finite element conveying fluid, suitable for modeling large deformations in the framework of Bernoulli Euler beam theory, is presented. The element is based on a third order planar beam finite element, introduced by Berzeri and Shabana, on basis of the absolute nodal coordinate formulation. The equations of motion for the pipe-element are derived using an extended version of Lagrange’s equations of the second kind for taking into account the flow of fluids, in contrast to the literature, where most derivations are based on Hamilton’s Principle or Newtonian approaches. The advantage of this element in comparison to classical large deformation beam elements, which are based on rotations, is the direct interpolation of position and directional derivatives, which simplifies the equations of motion considerably. As an advantage Lagrange’s equations of the second kind offer a convenient connection for introducing fluids into multibody dynamic systems. Standard numerical examples show the convergence of the deformation for increasing number of elements. For a cantilever pipe, the critical flow velocities for increasing number of pipe elements are compared to existing works, based on Euler elastica beams and moving discrete masses. The results show good agreements with the reference solutions applying only a small number of pipe finite elements.

A Large Deformation Planar Finite Element for Pipes Conveying Fluid Based on the Absolute Nodal Coordinate Formulation

2009 ◽  
Vol 4 (3) ◽  
Author(s):  
Michael Stangl ◽  
Johannes Gerstmayr ◽  
Hans Irschik
Keyword(s):  
Finite Element ◽  
Large Deformation ◽  
Absolute Nodal Coordinate Formulation ◽  
Equations Of Motion ◽  
Directional Derivatives ◽  
Absolute Nodal Coordinate ◽  
Lagrange’S Equations ◽  
The Absolute ◽  
Lagrange's Equations ◽  
Conveying Fluid

A novel planar pipe finite element conveying fluid with steady flow, suitable for modeling large deformations in the framework of the Bernoulli–Euler beam theory, is presented. The element is based on a third order planar beam finite element, introduced by Berzeri and Shabana (2000, “Development of Simple Models for the Elastic Forces in the Absolute Nodal Co-Ordinate Formulation,” J. Sound Vib., 235(4), pp. 539–565), applying the absolute nodal coordinate formulation. The equations of motion of the pipe finite element are derived using an extended version of Lagrange’s equations of the second kind taking into account the flow of fluid; in contrast, most derivations in the literature are based on Hamilton’s principle or the Newtonian approaches. The advantage of this element in comparison to classical large deformation beam elements, which are based on rotations, is the direct interpolation of position and directional derivatives, which simplifies the equations of motion considerably. As an advantage, Lagrange’s equations of the second kind offer a convenient connection for introducing fluids into multibody dynamic systems. Standard numerical examples show the convergence of the deformation for increasing number of elements. For a cantilever pipe, the critical flow velocities for increasing number of pipe elements are compared with existing works, based on Euler elastica beams and moving discrete masses. The results show good agreement with the reference solutions applying only a small number of pipe finite elements.

Stability analysis of a pipe conveying fluid with a nonlinear energy sink

2021 ◽  
Vol 64 (5) ◽  
Author(s):  
Nan Duan ◽  
Sida Lin ◽  
Yuhu Wu ◽  
Xi-Ming Sun ◽  
Chongquan Zhong
Keyword(s):  
Stability Analysis ◽  
Nonlinear Energy Sink ◽  
Pipe Conveying Fluid ◽  
Energy Sink ◽  
Nonlinear Energy ◽  
Conveying Fluid

Hopf-Hopf interactions in a spring-supported pipe conveying fluid

2021 ◽  
Vol 152 ◽  
pp. 107390
Author(s):  
K. Yamashita ◽  
N. Nishiyama ◽  
K. Katsura ◽  
H. Yabuno
Keyword(s):  
Pipe Conveying Fluid ◽  
Conveying Fluid
Sign in / Sign up

Export Citation Format

Share Document