New insight into the stability and dynamics of fluid-conveying supported pipes with small geometric imperfections

AbstractIn several previous studies, it was reported that a supported pipe with small geometric imperfections would lose stability when the internal flow velocity became sufficiently high. Recently, however, it has become clear that this conclusion may be at best incomplete. A reevaluation of the problem is undertaken here by essentially considering the flow-induced static deformation of a pipe. With the aid of the absolute nodal coordinate formulation (ANCF) and the extended Lagrange equations for dynamical systems containing non-material volumes, the nonlinear governing equations of a pipe with three different geometric imperfections are introduced and formulated. Based on extensive numerical calculations, the static equilibrium configuration, the stability, and the nonlinear dynamics of the considered pipe system are determined and analyzed. The results show that for a supported pipe with the geometric imperfection of a half sinusoidal wave, the dynamical system could not lose stability even if the flow velocity reaches an extremely high value of 40. However, for a supported pipe with the geometric imperfection of one or one and a half sinusoidal waves, the first-mode buckling instability would take place at high flow velocity. Moreover, based on a further parametric analysis, the effects of the amplitude of the geometric imperfection and the aspect ratio of the pipe on the static deformation, the critical flow velocity for buckling instability, and the nonlinear responses of the supported pipes with geometric imperfections are analyzed.

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

Applied Sciences ◽

10.3390/app12020724 ◽

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.

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Nonlinear Planar Dynamics of Fluid-Conveying Cantilevered Extensible Pipes

Volume 4A: Dynamics, Vibration and Control ◽

10.1115/imece2013-65785 ◽

2013 ◽

Author(s):

Mergen H. Ghayesh ◽

Michael P. Païdoussis ◽

Marco Amabili

Keyword(s):

Flow Velocity ◽

Trivial Solution ◽

Equations Of Motion ◽

Continuation Method ◽

Time Integration ◽

Axial Direction ◽

Transverse Displacement ◽

Lagrange Equations ◽

Critical Flow Velocity ◽

The Stability

This paper for the first time investigates the nonlinear planar dynamics of a cantilevered extensible pipe conveying fluid; the centreline of the pipe is considered to be extensible resulting in coupled longitudinal and transverse equations of motion; specifically, the kinetic and potential energies are obtained in terms of longitudinal and transverse displacements and then the extended version of the Lagrange equations for systems containing non-material volumes is employed to derive the equations of motion. Direct time integration along with the pseudo-arclength continuation method are employed to solve the discretized equations of motion. Bifurcation diagrams of the system are constructed as the flow velocity is increased as the bifurcation parameter. As opposed to the case of an inextensible pipe, an extensible pipe elongates in the axial direction as the flow velocity is increased from zero. At the critical flow velocity, the stability of the system is lost via a supercritical Hopf bifurcation, emerging from the trivial solution for the transverse displacement and non-trivial solution for the longitudinal displacement and leading to a flutter.

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Thermal-Nonlocal Vibration and Instability of Single-Walled Carbon Nanotubes Conveying Fluid

Journal of Mechanics ◽

10.1017/jmech.2011.59 ◽

2011 ◽

Vol 27 (4) ◽

pp. 567-573 ◽

Cited By ~ 9

Author(s):

T.-P. Chang

Keyword(s):

Flow Velocity ◽

Elastic Medium ◽

Natural Frequency ◽

Temperature Change ◽

Nonlocal Parameter ◽

Critical Flow ◽

Critical Flow Velocity ◽

Buckling Instability ◽

Single Walled Carbon ◽

Conveying Fluid

ABSTRACTAn elastic Bernoulli–Euler beam model is developed for thermal-mechanical vibration and buckling instability of a single-walled carbon nanotube (SWCNT) conveying fluid and resting on an elastic medium by using the theories of thermal elasticity mechanics and nonlocal elasticity. The differential quadrature method is adopted to obtain the numerical solutions to the model. The effects of temperature change, nonlocal parameter and elastic medium constant on the vibration frequency and buckling instability of SWCNT conveying fluid are investigated. It can be concluded that at low or room temperature, the first natural frequency and critical flow velocity for the SWCNT increase as the temperature change increases, on the contrary, while at high temperature the first natural frequency and critical flow velocity decrease with the increase of the temperature change. The first natural frequency for the SWCNT decreases as the nonlocal parameter increases, both the first natural frequency and critical flow velocity increase with the increase of the elastic medium constant.

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EFFECTS OF TIP MASS ON STABILITY OF ROTATING CANTILEVER PIPE CONVEYING FLUID WITH CRACK

International Journal of Modern Physics B ◽

10.1142/s0217979210065349 ◽

2010 ◽

Vol 24 (15n16) ◽

pp. 2609-2614 ◽

Cited By ~ 4

Author(s):

IN SOO SON ◽

HAN IK YOON ◽

SANG PIL LEE ◽

DONG JIN KIM

Keyword(s):

Angular Velocity ◽

Equations Of Motion ◽

Pipe Conveying Fluid ◽

Mass Ratio ◽

Critical Flow Velocity ◽

Pipe System ◽

Stability Maps ◽

The Stability ◽

Tip Mass ◽

Conveying Fluid

In this paper, the dynamic stability of a rotating cantilever pipe conveying fluid with a crack and tip mass is investigated by numerical method. That is, the effects of the rotating the rotating angular velocity, the mass ratio, the crack and tip mass on the critical flow velocity for flutter instability of system are studied. The equations of motion of rotating pipe are derived by using the extended Hamilton's principle. The crack section of pipe is represented by a local flexibility matrix connecting two undamaged pipe segments. The crack is assumed to be in the first mode of fracture and always opened during the vibrations. Finally, the stability maps of the cracked rotating pipe system as a rotating angular velocity and mass ratio β are presented.

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Basic Study on Mitigation of Annular-Flow-Induced Vibration by Considering Variability in Parameters of Structure and Fluid

Volume 4: Fluid-Structure Interaction ◽

10.1115/pvp2013-97845 ◽

2013 ◽

Author(s):

Atsuhiko Shintani ◽

Hirokazu Isono ◽

Tomohiro Ito ◽

Chihiro Nakagawa

Keyword(s):

Flow Velocity ◽

Annular Flow ◽

Coupled System ◽

Critical Flow ◽

Control Input ◽

Navier Stokes Equation ◽

Critical Flow Velocity ◽

Fluid Structure ◽

The Stability ◽

Coupled Equation

In this study, the stability of a structure and mitigation of the vibration of a structure subjected to annular flow are investigated when the parameters of the structure and fluid have variability or uncertainty. The equations of motion of the structure and fluid are given by the Euler-Bernoulli-type partial differential equation and the Navier–Stokes equation, respectively. Hence, the fluid–structure coupled system has variability. The fluid–structure coupled equation considering variability is derived from the above-mentioned equations. By drawing the root locus of the coupled equation, the stability of the coupled system with variability is investigated. Because the parameters of structure and fluid have variability, the critical flow velocity also varies. The effect of parameter variability on the critical flow velocity variability is investigated. Furthermore, to reduce the coupled vibration of the system with variability, a control input is used. Through adequate control, the coupled system with variability is stabilized.

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Nonlinear Vibration and Stability Analysis of Embedded Carbon Nanotubes With Internal Flow

ASME 2010 10th Biennial Conference on Engineering Systems Design and Analysis, Volume 5 ◽

10.1115/esda2010-25370 ◽

2010 ◽

Author(s):

M. Rasekh ◽

S. E. Khadem

Keyword(s):

Carbon Nanotube ◽

Nonlinear Vibration ◽

Elastic Medium ◽

Multiple Scales ◽

Internal Flow ◽

Beam Theory ◽

Response Curves ◽

Critical Flow Velocity ◽

Aspect Ratios ◽

The Stability

In this paper, for the first time, the influence of internal moving fluid on the nonlinear vibration and stability of embedded carbon nanotube is investigated. The Euler-Bernoulli beam theory is employed to model the vibrational behavior of an embedded carbon nanotube. The relationship of nonlinear amplitude and frequency for the single-wall nanotubes in the presence of internal fluid flow is expressed using the multiple scales perturbation method. The amplitude-frequency response curves of the nonlinear vibration obtained and the effects of the surrounding elastic medium, mass and the aspect ratios of nanotubes are discussed. It is shown that beyond the critical flow velocity buckling occurs and surrounding elastic medium plays a significant role in the stability of the carbon nanotube.

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A Model for the Nonlinear Buckling of Human Aorta

Volume 4: Dynamics, Control and Uncertainty, Parts A and B ◽

10.1115/imece2012-89141 ◽

2012 ◽

Author(s):

Marco Amabili ◽

Kostas Karazis ◽

Rosaire Mongrain ◽

Nastaran Shahmansouri

Keyword(s):

Blood Flow ◽

Flow Velocity ◽

Stokes Equations ◽

Surrounding Tissue ◽

Human Aorta ◽

Critical Flow ◽

Linear Potential ◽

Critical Flow Velocity ◽

Aortic Segment ◽

The Stability

Human aortas are subjected to large mechanical stresses due to blood flow pressurization and through contact with the surrounding tissue. It is essential that the aorta does not lose stability by buckling for its proper functioning to ensure proper blood flow. A refined reduced-order bifurcation analysis model is employed to examine the stability of an aortic segment subjected to internal blood flow. The structural model is based on a nonlinear cylindrical orthotropic laminated composite shell theory that assumes three aortic wall layers representing the tunica intima, media and adventitia. The fluid model contains the unsteady effects obtained from linear potential flow theory and the steady viscous effects obtained from the time-averaged Navier-Stokes equations. Residual stresses due to pressurization are evaluated and included in the model. The aortic segment loses stability by divergence with deformation of the cross-section at a critical flow velocity for a given static pressure, exhibiting a strong subcritical behaviour with partial or total collapse of the inner wall. Subsequent analyses including the effect of geometric wall imperfections indicate that imperfections in the axial direction have a more profound effect on the stability of the aorta decreasing the critical flow velocity for buckling.

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Numerical Study of Thermal Effect on the Stability of Carbon Nanotubes Resting on a Viscoelastic Foundation Subjected to Magnetic Field

International Journal of Structural Stability and Dynamics ◽

10.1142/s0219455422500249 ◽

2021 ◽

Author(s):

Zeinab Heidary ◽

Afsaneh Mojra

Keyword(s):

Magnetic Field ◽

Carbon Nanotubes ◽

Fluid Flow ◽

Flow Velocity ◽

Temperature Variation ◽

Critical Flow ◽

Viscoelastic Foundation ◽

Critical Flow Velocity ◽

The Stability ◽

The Magnetic Field

Carbon nanotubes (CNTs) have emerged as efficient tools in drug delivery systems; therefore, it is essential to refer to the importance of the magnetic field, in addition to the fluid flow on the dynamic behavior of CNTs. Additionally, in such medical applications, the actual working environment of nanotube often contains temperature changes, and CNTs are surrounded by soft tissues with viscoelastic mechanical properties. In this study, the vibrational behavior of CNTs conveying magnetic-fluid flow and resting on a viscoelastic foundation is investigated under various temperature variations. To incorporate the influence of slip velocity at the nanoscale, a correction factor is employed on the basis of the Beskok–Karniadakis model. The nanotube is modeled by the Euler–Bernoulli beam theory, and governing equations of motion are derived by implementing Hamilton’s principle based on Eringen’s nonlocal elasticity theory. Results indicate that by applying a magnetic field with an intensity of 30[Formula: see text]T, the dimensionless critical flow velocity increases from 4.345 to 12.603. Also, the critical flow velocity shows an increase from 4.345 to 5.854 in the presence of a viscoelastic foundation. Furthermore, a temperature variation equal to 20[Formula: see text]K reduces the critical flow velocity dramatically from 4.345 to 1.802 at low temperatures, while an increase from 4.345 to 5.443 is observed at high temperatures. Consequently, while the magnetic field and the viscoelastic foundation affect the system stability, the temperature variation may improve or deteriorate the stability. Therefore, to plan for a medical application, the inclusion of temperature variation is required.

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Stability and Modal Conversion Phenomenon of Pipe-in-Pipe Structures with Arbitrary Boundary Conditions by Means of Green’s Functions

International Journal of Structural Stability and Dynamics ◽

10.1142/s0219455422500341 ◽

2021 ◽

Author(s):

Xueping Chang ◽

Jinming Fan ◽

Duzheng Han ◽

Bo Chen ◽

Yinghui Li

Keyword(s):

Boundary Conditions ◽

Flow Velocity ◽

Volume Fraction ◽

Frequency Equation ◽

Stiffness Coefficient ◽

Equivalent Stiffness ◽

Critical Flow Velocity ◽

Arbitrary Boundary ◽

The Stability ◽

Single Pipe

In this paper, a closed-form frequency equation of the pipe-in-pipe (PIP) structure with arbitrary boundaries is obtained. The frequency equation is derived from Green’s function of the transverse forced vibration of the PIP structure and takes into account the effects of internal two-phase flow and axial pressure. The reliability of the method in this paper is proved by comparison with the published literature. In the numerical discussion part, the PIP structures with clamped-clamped, clamped-free, and elastic boundary conditions are used as examples to discuss. The effects of equivalent stiffness coefficient, internal flow velocity, and gas volume fraction on the stability of PIP structure are studied. The results show that the stability of the PIP structure is better than that of the single-pipe structure, and the greater the equivalent stiffness coefficient of the elastic layer, the higher the critical flow velocity of the structure. In addition, a modal conversion phenomenon existing in the PIP structure is discovered. There are different forms of modal conversion for different boundary conditions, and the modal conversion makes the order of instability of the PIP structure different from that of a single-pipe. The conclusion of this paper has positive significance for the dynamic research of PIP structure.

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