A Hybrid Ale Formulation for the Investigation of the Stability of Pipes Conveying Fluid and Axially Moving Beams

2022 ◽  
Author(s):  
Michael Pieber ◽  
Konstantina Ntarladima ◽  
Robert Winkler ◽  
Johannes Gerstmayr
Keyword(s):  
Equations Of Motion ◽  
Arbitrary Lagrangian Eulerian ◽  
Multibody Modeling ◽  
Ale Formulation ◽  
Conveyor Belts ◽  
Axially Moving Beams ◽  
Pipes Conveying Fluid ◽  
Axially Moving ◽  
The Stability ◽  
Conveying Fluid

Abstract The present work addresses pipes conveying fluid and axially moving beams undergoing large deformations. A novel two dimensional beam finite element is presented, based on the Absolute Nodal Coordinate Formulation (ANCF) with an extra Eulerian coordinate to describe axial motion. The resulting formulation is well known as Arbitrary Lagrangian Eulerian (ALE) method, which is often used to model axially moving beams and pipes conveying fluid. The proposed approach, which is derived from an extended version of Lagrange's equations of motion, allows for the investigation of the stability of pipes conveying fluid and axially moving beams for a certain axial velocity and stationary state of large deformation. Additionally, a multibody modeling approach allows us to extend the beam formulation for co-moving discrete masses, which represent concentrated masses attached to the beam, e.g., gondolas in ropeway systems, or transported masses in conveyor belts. Within numerical investigations, we show that axially moving beams and a larger number of discrete masses behave similarly as the case of (continuously) distributed mass.

Investigation of the Stability of Axially Moving Beams With Discrete Masses

2021 ◽  
Author(s):  
Konstantina Ntarladima ◽  
Michael Pieber ◽  
Johannes Gerstmayr
Keyword(s):  
Large Deformations ◽  
Equations Of Motion ◽  
Arbitrary Lagrangian Eulerian ◽  
Axial Motion ◽  
Multibody Modeling ◽  
Conveyor Belts ◽  
Axially Moving Beams ◽  
Concentrated Masses ◽  
Axially Moving ◽  
The Stability

Abstract The present paper addresses axially moving beams with co-moving concentrated masses while undergoing large deformations. For the numerical modeling, a novel beam finite element is introduced, which is based on the absolute nodal coordinate formulation extended with an additional Eulerian coordinate to represent the axial motion. The resulting formulation is well known as Arbitrary Lagrangian Eulerian (ALE) method, which is often used for axially moving beams and pipes conveying fluids. As compared to previous formulations, the present formulation allows us to introduce the Eulerian part by an independent coordinate, which fully incorporates the dynamics of the axial motion, while the shape functions remain independent of the beam coordinates and are thus constant. The proposed approach, which is derived from an extended version of Lagrange’s equations of motion, allows for the investigation of the stability of axially moving beams for a certain axial velocity and stationary state of large deformation. A multibody modeling approach allows us to extend the beam formulation for co-moving discrete masses, which represent concentrated masses attached to the beam, e.g., gondolas in ropeway systems, or transported masses in conveyor belts. Within numerical investigations we show that a larger number of discrete masses behaves similarly as the case of (continuously) distributed mass along the beam.

Dynamics and Stability of Pipes Conveying Fluid

1994 ◽  
Vol 116 (1) ◽  
pp. 57-66 ◽  
Author(s):  
C. O. Chang ◽  
K. C. Chen
Keyword(s):  
Equations Of Motion ◽  
Stability Boundary ◽  
Harmonic Component ◽  
Mean Value ◽  
Transverse Motion ◽  
Perturbation Techniques ◽  
Damped System ◽  
Pipes Conveying Fluid ◽  
The Stability ◽  
Conveying Fluid

This paper deals with the dynamics and stability of simply supported pipes conveying fluid, where the fluid has a small harmonic component of flow velocity superposed on a constant mean value. The perturbation techniques and the method of averaging are used to convert the nonautonomous system into an autonomous one and determine the stability boundaries. Post-bifurcation analysis is performed for the parametric points in the resonant regions where the axial force, which is induced by the transverse motion of the pipe due to the fixed-span ends and contributes nonlinearities to the equations of motion, is included. For the undamped system, linear analysis is inconclusive about stability and there does not exist nontrivial solution in the resonant regions. For the damped system, it is found that the original stable system remains stable when the pulsating frequency increases cross the stability boundary and becomes unstable when the pulsating frequency decreases cross the stability boundary.

Influence of Nonlinearities on the Behavior of Parametrically Excited Articulated Pipes Conveying Fluid

1978 ◽  
Vol 5 (1) ◽  
pp. 31-38 ◽  
Author(s):  
J. Rousselet ◽  
G. Herrmann
Keyword(s):  
Fluid Flow ◽  
Stability Analysis ◽  
Dynamic Systems ◽  
Linear Formulation ◽  
Fluctuating Pressure ◽  
The Past ◽  
Pipes Conveying Fluid ◽  
Critical Velocities ◽  
The Stability ◽  
Conveying Fluid

This paper presents the analysis of a system of articulated pipes hanging vertically under the influence of gravity. The liquid, driven by a slightly fluctuating pressure, circulates through the pipes. Similar systems have been analysed in the past by numerous authors but a common feature of their work is that the behavior of the fluid flow is prescribed, rather than left to be determined by the laws of motion. This leads to a linear formulation of the problem which can not predict the behavior of the system for finite amplitudes of motion. A circumstance in which this behavior is important arises in the stability analysis of the system in the neighbourhood of critical velocities, that is, flow velocities at which the system starts to flutter. Hence, the purpose of the present study was to investigate in greater detail the region close to critical velocities in order to find by how much these critical velocities would be affected by the amplitudes of motion. This led to a set of three coupled-nonlinear equations, one of which represents the motion of the fluid. In the mathematical development, use is made of a scheme which permits the uncoupling of the modes of motion of damped nonconservative dynamic systems. Results are presented showing the importance of the nonlinearities considered.

Kinematic Aspects in Modeling Large-Amplitude Vibration of Axially Moving Beams

2019 ◽  
Vol 11 (02) ◽  
pp. 1950021 ◽  
Author(s):  
Yuanbin Wang ◽  
Hu Ding ◽  
Li-Qun Chen
Keyword(s):  
Large Amplitude ◽  
Model Equation ◽  
Classical Model ◽  
Equations Of Motion ◽  
Beam Theory ◽  
Governing Equations ◽  
Amplitude Vibration ◽  
Large Amplitude Vibration ◽  
Axially Moving Beams ◽  
Axially Moving

This paper clarified kinematic aspects of motion of axially moving beams undergoing large-amplitude vibration. The kinematics was formulated in the mixed Eulerian–Lagrangian framework. Based on the kinematic analysis, the governing equations of nonlinear vibration were derived from the extended Hamilton principle and the higher-order shear beam theory. The derivation considered the effects of material parameters on the beam deformation. The proposed governing equations were compared with a few previous governing equations. The comparisons show that proposed equations are with higher precision. Besides, the proposed equations can be viewed as the asymptotic governing equations of Lagrange’s equations of motion for large displacement. Finally, the corresponding boundary conditions and the comparison between the presented model equation and classical model equation were provided.

scholarly journals Influence of Dry Friction on the Dynamics of Cantilevered Pipes Conveying Fluid

2022 ◽  
Vol 12 (2) ◽  
pp. 724
Author(s):  
Zilong Guo ◽  
Qiao Ni ◽  
Lin Wang ◽  
Kun Zhou ◽  
Xiangkai Meng
Keyword(s):  
Flow Velocity ◽  
Friction Force ◽  
Dry Friction ◽  
Critical Flow Velocity ◽  
Pipe System ◽  
Pipes Conveying Fluid ◽  
Cantilevered Pipe ◽  
The Stability ◽  
Friction Parameters ◽  
Conveying Fluid

A cantilevered pipe conveying fluid can lose stability via flutter when the flow velocity becomes sufficiently high. In this paper, a dry friction restraint is introduced for the first time, to evaluate the possibility of improving the stability of cantilevered pipes conveying fluid. First, a dynamical model of the cantilevered pipe system with dry friction is established based on the generalized Hamilton’s principle. Then the Galerkin method is utilized to discretize the model of the pipe and to obtain the nonlinear dynamic responses of the pipe. Finally, by changing the values of the friction force and the installation position of the dry friction restraint, the effect of dry friction parameters on the flutter instability of the pipe is evaluated. The results show that the critical flow velocity of the pipe increases with the increment of the friction force. Installing a dry friction restraint near the middle of the pipe can significantly improve the stability of the pipe system. The vibration of the pipe can also be suppressed to some extent by setting reasonable dry friction parameters.

scholarly journals Parametric Vibrations of Axially Moving Beams with Multiple Edge Cracks

2019 ◽  
Vol 24 (2) ◽  
pp. 241-252 ◽  
Author(s):  
Murat Sarıgül
Keyword(s):  
Natural Frequencies ◽  
Equations Of Motion ◽  
Crack Depth ◽  
Multiple Cracks ◽  
Mean Velocity ◽  
Beam System ◽  
Crack Tips ◽  
Axially Moving Beams ◽  
Edge Cracks ◽  
Axially Moving

Nonlinear transverse vibrations of axially moving beams with multiple cracks is handled studied. Assuming that the beam moves with mean velocity having harmonically variation, influence of the edge crack on the moving continua are investigated in this study. Due to existence of the crack in the transverse direction, the healthily beam is divided into parts. The translational and rotational springs are replaced between these parts so that high stressed regions around the crack tips are redefined with the springs' energies. Thus, the problem is converted to an axially moving spring-beam system. The equations of motion and its corresponding conditions are obtained by means of the Hamilton Principle. In numerical analysis, the natural frequencies and responses of the spring-beam system are investigated for principal parametric resonance in detail. Some important results are obtained; the natural frequencies decreases with increasing crack depth. In case of the beam travelling with high velocities, the effects of crack's depth on natural frequencies seems to be vanished.

scholarly journals Stability Analysis of Fluid-Conveying Beams using Artificial Intelligence

2018 ◽  
Vol 3 (1) ◽  
Author(s):  
Theddeus T Akano ◽  
Olumuyiwa S Asaolu
Keyword(s):  
Artificial Intelligence ◽  
Fuzzy Inference ◽  
Fuzzy Model ◽  
Inference System ◽  
Fluid Field ◽  
Neuro Fuzzy ◽  
Pipes Conveying Fluid ◽  
The Stability ◽  
Stability Results ◽  
Conveying Fluid

This paper employs artificial intelligence in predicting the stability of pipes conveying fluid. Field data was collected for different pipe structures and usage. Adaptive Neuro-Fuzzy Inference System (ANFIS) model is implemented to predict the stability of the pipe using the fundamental natural frequency at different flow velocities as the index of stability. Results reveal that the neuro-fuzzy model compares relatively well with the conventional finite element method. It was also established that a pipe conveying fluid is most stable when the pipe is clamped at both ends but least stable when it is a cantilever.

Nonlinear Free Vibration of Spinning Viscoelastic Pipes Conveying Fluid

2018 ◽  
Vol 10 (07) ◽  
pp. 1850076 ◽  
Author(s):  
Feng Liang ◽  
Xiao-Dong Yang ◽  
Wei Zhang ◽  
Ying-Jing Qian
Keyword(s):  
Oil And Gas ◽  
Multiple Scales ◽  
Equations Of Motion ◽  
Drill String ◽  
Mode Shapes ◽  
Flowing Fluid ◽  
Nonlinear Dynamical ◽  
Pipes Conveying Fluid ◽  
Spinning Speed ◽  
Conveying Fluid

Drill strings are one of the most significant rotor components employed in oil and gas exploitation. In this paper, an improved dynamical model of drill-string-like pipes conveying fluid is developed by taking into account the axial spin, fluid–structure interaction (FSI), damping as well as curvature and inertia nonlinearities. The partial differential equations of motion are derived by two sequential Euler angles and the Hamilton principle and then directly handled by the multiple scales method. The nonlinear amplitudes, frequencies and whirling mode shapes are all investigated towards various system parameters to display the nonlinear dynamical characteristics of such a special rotor system coupled with FSI. It is revealed that the nonlinear amplitudes and frequencies are explicitly dependent on the spinning speed, while the flowing fluid mainly contributes to the linear frequencies, and consequently influences the nonlinear amplitudes and frequencies. The FSI effect and axial spin can both improve the forward procession mode and suppress the backward one, while both procession modes will be suppressed by the viscoelastic damping. The pipe will ultimately present a forward as well as decayed whirling motion for the fundamental mode.

Dynamic Stability of Periodic Pipes Conveying Fluid

2013 ◽  
Vol 81 (1) ◽  
Author(s):  
Dianlong Yu ◽  
Michael P. Païdoussis ◽  
Huijie Shen ◽  
Lin Wang
Keyword(s):  
Material Properties ◽  
Unit Length ◽  
Mass Parameter ◽  
High Accuracy ◽  
Pipe Conveying Fluid ◽  
Good Convergence ◽  
System Parameters ◽  
Pipes Conveying Fluid ◽  
The Stability ◽  
Conveying Fluid

In this paper, the stability of a periodic cantilevered pipe conveying fluid is studied theoretically by means of a novel transfer matrix method. This method is first validated by comparing the results to those available in the literature for a uniform pipe, showing that it is capable of high accuracy and displaying good convergence characteristics. Then, the stability of periodic pipes is investigated, with geometric, material-properties periodicity, and a combination of the two, showing that a considerable stabilizing effect may be achieved over different ranges of the mass parameter β (β=mf/(mf+mp), where mf and mp are the fluid and pipe masses per unit length). The effect of other different system parameters is also probed.

Sign in / Sign up

Export Citation Format

Share Document