Vibration and Stability of Helical Pipes Conveying Fluid

1987 ◽  
Vol 109 (4) ◽  
pp. 402-410 ◽  
Author(s):  
C.-N. Fan ◽  
W.-H. Chen
Keyword(s):  
Natural Frequencies ◽  
Equations Of Motion ◽  
Mode Shapes ◽  
Critical Flow ◽  
Helical Pipe ◽  
End Conditions ◽  
Finite Element Procedure ◽  
Pipes Conveying Fluid ◽  
Conveying Fluid ◽  
Flow Velocities

This paper presents an accurate finite element procedure for the vibration and stability analysis of helical pipe conveying fluid. The kinematics of the helical pipe are derived including the effects of arbitrary curvatures and torsions in a nonorthogonal helical coordinate system. The equations of motion are derived from the Hamilton’s principle for mass transport system and the shear deformation and rotary inertia are also considered. The 3-node space-curved isoparametric element is used. The natural frequencies, mode shapes and critical flow velocities of buckling are studied for different end conditions. The significant influence of torsion effects on the calculation of natural frequencies and critical flow velocities is found. To demonstrate the validity and accuracy of the techniques developed, several numerical examples are illustrated.

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.

An Analytical Study of the Dynamics of Pipes Conveying Fluid of Axially Varying Density

2010 ◽  
Author(s):  
Dana Giacobbi ◽  
Christian Semler ◽  
Michael Pai¨doussis
Keyword(s):  
Analytical Study ◽  
Critical Flow ◽  
General Interest ◽  
Constant Density ◽  
Flexible Pipe ◽  
Analytical Perspective ◽  
Pipes Conveying Fluid ◽  
Cantilevered Pipe ◽  
Conveying Fluid ◽  
Flow Velocities

This paper investigates the dynamics of a slender, flexible pipe, conveying a fluid whose density varies axially along the length of the pipe. Specific applications for this system have appeared in the mining of submerged methane crystals [1], but a general interest also exists due to more common situations in which fluid density changes along the length of the pipe, such as when a gas is conveyed at high velocity. Therefore, following a brief review of related work and of the well-established theory concerning pipes conveying fluid of constant density, the current problem is approached from an analytical perspective. In particular, a linear model describing the system is derived using a Hamiltonian approach, for the cases of (i) a pipe clamped at both ends and (ii) a cantilevered pipe, and results obtained using a Galerkin approach. Ultimately, it is shown that, in both the cantilevered and clamped-clamped cases, the behaviour of the system is similar to that of a pipe conveying fluid of constant density — that is, loss of stability by flutter and buckling respectively — save for two crucial differences. The first and most important is that it is the density at the discharging end which has the most significant effect on the critical flow velocities, rather than any other. Second, in the case of a cantilevered pipe, the magnitude of the density change can strongly influence in which mode the system loses stability, thereby also impacting the critical flow velocities. The specifics of both these effects are addressed in the paper.

scholarly journals A New Method Based on Laplace Transform and Its Application to Stability of Pipe Conveying Fluid

2017 ◽  
Vol 2017 ◽  
pp. 1-9
Author(s):  
H. B. Wen ◽  
Y. R. Yang ◽  
P. Li ◽  
Y. D. Li ◽  
Y. Huang
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Present Method ◽  
Natural Frequencies ◽  
Vibration Mode ◽  
Transformation Method ◽  
Critical Flow ◽  
Pipe Conveying Fluid ◽  
Pipes Conveying Fluid ◽  
Conveying Fluid

A new differential transformation method is developed in this paper and is applied for free vibration problem of pipes conveying fluid. The natural frequencies, critical flow velocities, and vibration mode functions of such pipes with several typical boundary conditions are obtained and compared with the results predicted by Galerkin method and finite element method (FEM) and with other results archived. The results show that the present method is of high precision and can serve as an analytical method for the vibration of pipes conveying fluid.

scholarly journals Observations on the vibration of axially tensioned elastomeric pipes conveying fluid

2000 ◽  
Vol 214 (3) ◽  
pp. 423-434 ◽  
Author(s):  
Y L Zhang ◽  
D G Gorman ◽  
J M Reese ◽  
J Horacek
Keyword(s):  
Mathematical Model ◽  
Penalty Function ◽  
Natural Frequencies ◽  
Mode Shapes ◽  
Function Technique ◽  
Flowing Fluid ◽  
Linear Dynamic ◽  
Axial Tension ◽  
Pipes Conveying Fluid ◽  
Conveying Fluid

A study of the effect of axial tension on the vibration of a single-span elastomeric pipe clamped at both ends conveying fluid has been carried out both experimentally and theoretically. A new mathematical model using a penalty function technique and the method of kinematic correction and fictitious loads has been developed. The influence of flowing fluid and axial tension on natural frequencies and mode shapes of the system has been described using this model and compared with experimental observations. Linear and non-linear dynamic response of the harmonically excited pipe has also been investigated for varying flow velocities and initial axial tensions.

scholarly journals Effect of Thrust on the Structural Vibrations of a Nonuniform Slender Rocket

2020 ◽  
Vol 25 (2) ◽  
pp. 29
Author(s):  
Desmond Adair ◽  
Aigul Nagimova ◽  
Martin Jaeger
Keyword(s):  
Natural Frequencies ◽  
Equations Of Motion ◽  
Approximate Solutions ◽  
Mode Shapes ◽  
Algebraic Equations ◽  
Structural Vibrations ◽  
Unknown Parameters ◽  
One Dimensional ◽  
Vibration Problems ◽  
Nonuniform Beam

The vibration characteristics of a nonuniform, flexible and free-flying slender rocket experiencing constant thrust is investigated. The rocket is idealized as a classic nonuniform beam with a constant one-dimensional follower force and with free-free boundary conditions. The equations of motion are derived by applying the extended Hamilton’s principle for non-conservative systems. Natural frequencies and associated mode shapes of the rocket are determined using the relatively efficient and accurate Adomian modified decomposition method (AMDM) with the solutions obtained by solving a set of algebraic equations with only three unknown parameters. The method can easily be extended to obtain approximate solutions to vibration problems for any type of nonuniform beam.

Free Vibration Analysis of a Carbon Nanotube Reinforced Composite Beam

2014 ◽  
Vol 592-594 ◽  
pp. 2041-2045 ◽  
Author(s):  
B. Naresh ◽  
A. Ananda Babu ◽  
P. Edwin Sudhagar ◽  
A. Anisa Thaslim ◽  
R. Vasudevan
Keyword(s):  
Carbon Nanotube ◽  
Free Vibration ◽  
Composite Beam ◽  
Natural Frequencies ◽  
Equations Of Motion ◽  
Free Vibration Analysis ◽  
Mode Shapes ◽  
Element Formulation ◽  
Reinforced Composite ◽  
Vibration Responses

In this study, free vibration responses of a carbon nanotube reinforced composite beam are investigated. The governing differential equations of motion of a carbon nanotube (CNT) reinforced composite beam are presented in finite element formulation. The validity of the developed formulation is demonstrated by comparing the natural frequencies evaluated using present FEM with those of available literature. Various parametric studies are also performed to investigate the effect of aspect ratio and percentage of CNT content and boundary conditions on natural frequencies and mode shapes of a carbon nanotube reinforced composite beam. It is shown that the addition of carbon nanotube in fiber reinforced composite beam increases the stiffness of the structure and consequently increases the natural frequencies and alter the mode shapes.

A Unified Frequency Equation and the Motion Analysis of a Moving Flexible Beam Carrying a Concentrated Mass

1999 ◽  
Author(s):  
S. Park ◽  
J. W. Lee ◽  
Y. Youm ◽  
W. K. Chung
Keyword(s):  
Natural Frequencies ◽  
Equations Of Motion ◽  
Frequency Equation ◽  
Open Loop ◽  
Mode Shapes ◽  
Flexible Beam ◽  
Lumped Mass ◽  
Concentrated Mass ◽  
Forcing Function ◽  
The Mathematical Model

Abstract In this paper, the mathematical model of a Bernoulli-Euler cantilever beam fixed on a moving cart and carrying an intermediate lumped mass is derived. The equations of motion of the beam-mass-cart system is analyzed utilizing unconstrained modal analysis, and a unified frequency equation which can be generally applied to this kind of system is obtained. The change of natural frequencies and mode shapes with respect to the change of the mass ratios of the beam, the lumped mass and the cart and to the position of the lumped mass is investigated. The open-loop responses of the system by arbitrary forcing function are also obtained through numerical simulations.

scholarly journals Frequency Analysis of Functionally Graded Curved Pipes Conveying Fluid

2016 ◽  
Vol 2016 ◽  
pp. 1-9 ◽  
Author(s):  
Feng Liang ◽  
Xiao-Dong Yang ◽  
Ri-Dong Bao ◽  
Wei Zhang
Keyword(s):  
Natural Frequencies ◽  
Flexural Rigidity ◽  
Sensitivity Study ◽  
Functionally Graded ◽  
Opening Angle ◽  
Curved Pipes ◽  
Free Vibration Frequency ◽  
Pipes Conveying Fluid ◽  
Curved Pipes Conveying Fluid ◽  
Conveying Fluid

The curved pipe made of functionally graded material conveying fluid is considered and the in-plane free vibration frequency of the resulting composite pipe is investigated. The material properties are assumed to distribute continuously along the pipe wall thickness according to a power law and the effective mass, flexural rigidity, and mass ratio are used in the governing equations. The natural frequencies are derived numerically by applying the modified inextensible theory. The lowest four natural frequencies are studied via the complex mode method, the validity of which is demonstrated by comparing the results with those in available literatures. A parametric sensitivity study is conducted by numerical examples and the results obtained reveal the significant effects of material distribution gradient index, flow velocity, fluid density, and opening angle on the natural frequencies of the FGM curved pipes conveying fluid.

Nonlinear Vibrations of a Beam-Spring-Large Mass System

2017 ◽  
Author(s):  
Mohammad A. Bukhari ◽  
Oumar R. Barry
Keyword(s):  
Natural Frequencies ◽  
Multiple Scales ◽  
Equations Of Motion ◽  
Primary Resonance ◽  
Large Mass ◽  
Mode Shapes ◽  
Resonance Excitation ◽  
Response Curves ◽  
Mass System ◽  
Spring System

This paper presents the nonlinear vibration of a simply supported Euler-Bernoulli beam with a mass-spring system subjected to a primary resonance excitation. The nonlinearity is due to the mid-plane stretching and cubic spring stiffness. The equations of motion and the boundary conditions are derived using Hamiltons principle. The nonlinear system of equations are solved using the method of multiple scales. Explicit expressions are obtained for the mode shapes, natural frequencies, nonlinear frequencies, and frequency response curves. The validity of the results is demonstrated via comparison with results in the literature. Exact natural frequencies are obtained for different locations, rotational inertias, and masses.

Sign in / Sign up

Export Citation Format

Share Document