The effects of Knudsen-dependent flow velocity on vibrations of a nano-pipe 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.

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Parametric Resonances of a Cantilevered Pipe Conveying Fluid: A Nonlinear Analysis

Volume 3A: 15th Biennial Conference on Mechanical Vibration and Noise — Vibration of Nonlinear, Random, and Time-Varying Systems ◽

10.1115/detc1995-0272 ◽

1995 ◽

Author(s):

C. Semler ◽

M. P. Païdoussis

Keyword(s):

Flow Velocity ◽

Standard Form ◽

Harmonic Component ◽

Harmonic Balance Method ◽

Pipe Conveying Fluid ◽

Mean Flow ◽

Incremental Harmonic Balance Method ◽

Inertial Terms ◽

The Stability ◽

Conveying Fluid

Abstract This paper deals with the nonlinear dynamics and the stability of cantilevered pipes conveying fluid, where the fluid has a harmonic component of flow velocity, assumed to be small, superposed on a constant mean value. The mean flow velocity is near the critical value for which the pipe becomes unstable by flutter through a Hopf bifurcation. The partial differential equation is transformed into a set of ordinary differential equations (ODEs) using the Galerkin method. The equations of motion contain nonlinear inertial terms, and hence cannot be put into standard form for numerical integration. Various approaches are adopted to tackle the problem: (a) a perturbation method via which the nonlinear inertial terms are removed by finding an equivalent term using the linear equation; the system is then put into first-order form and integrated using a Runge-Kutta scheme; (b) a finite difference method based on Houbolt’s scheme, which leads to a set of nonlinear algebraic equations that is solved with a Newton-Raphson approach; (c) the stability boundaries are obtained using an incremental harmonic balance method as proposed by S.L. Lau. Using the three methods, the dynamics of the pipe conveying fluid is investigated in detail. For example, the effects of (i) the forcing frequency, (ii) the perturbation amplitude, and (iii) the flow velocity are considered. Particular attention is paid to the effects of the nonlinear terms. These results are compared with experiments undertaken in our laboratory, utilizing elastomer pipes conveying water. The pulsating component of the flow is generated by a plunger pump, and the motions are monitored by a noncontacting optical follower system. It is shown, both numerically and experimentally, that periodic and quasiperiodic oscillations can exist, depending on the parameters.

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Stabilization of a flexible pipe conveying fluid with an active boundary control method

Journal of Vibration and Control ◽

10.1177/1077546320907751 ◽

2020 ◽

Vol 26 (19-20) ◽

pp. 1824-1834

Author(s):

Beiming Yu ◽

Hiroshi Yabuno ◽

Kiyotaka Yamashita

Keyword(s):

Flow Velocity ◽

Control Method ◽

Bending Moment ◽

The Self ◽

Pipe Conveying Fluid ◽

Stabilization Method ◽

Critical Flow Velocity ◽

Complex Eigenvalues ◽

Excited Oscillation ◽

Conveying Fluid

A method of stabilizing the self-excited oscillation of a cantilevered pipe conveying fluid because of non–self-adjointness is proposed theoretically and experimentally. Complex eigenvalues denoting the natural frequency and damping of the system vary with an increase in the flow velocity. When the flow velocity exceeds a critical value, the flow-generated damping becomes negative and the pipe is dynamically destabilized. The complex eigenvalues with respect to flow velocity are affected by boundary conditions. We, thus, propose a stabilization control actuating the boundary condition. The stabilization method is carried out by applying a bending moment proportional to the bottom displacement of the pipe. The effect of the proposed control method is shown by investigating the stability for the three lowest modes of the system depending on the feedback gain. It is theoretically clarified that the critical flow velocity is increased by the proposed control method. Furthermore, experiments are performed using a fluid conveying pipe with two piezoactuators at the downstream end. The piezoactuators apply a bending moment at the downstream end of the pipe according to the theoretically proposed method. Experimental results verify that the proposed stabilization method suppresses the self-excited oscillation.

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Parametric and Combination Resonances of a Pipe Conveying Pulsating Fluid

Journal of Applied Mechanics ◽

10.1115/1.3423705 ◽

1975 ◽

Vol 42 (4) ◽

pp. 780-784 ◽

Cited By ~ 71

Author(s):

M. P. Paidoussis ◽

C. Sundararajan

Keyword(s):

Flow Velocity ◽

Parametric Resonance ◽

Mean Value ◽

Pipe Conveying Fluid ◽

Combination Resonance ◽

Load Combination ◽

Parametric Resonances ◽

The Difference ◽

Pulsating Fluid ◽

Conveying Fluid

In this paper we consider the dynamics of a pipe conveying fluid, when the flow velocity is harmonically perturbed about a mean value. Two methods of analysis are presented; Bolotin’s method, which can only give the boundaries of regions of parametric resonance, and a numerical Floquet analysis, which gives also the boundaries of combination resonance. A number of calculations for cantilevered pipes show that, generally, combination resonance is less important than parametric resonance, except for flow velocities near the critical (where the system loses stability in steady flow); parametric resonances are selectively associated with only some of the modes of the system, and combination resonances involve only the difference of the eigenfrequencies. For pipes clamped at both ends the behavior of the system is similar to that of a column subjected to a pulsating load; combination resonances in this case involve the sum of the eigenfrequencies.

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Dynamic Behavior of Continuous Cantilevered Pipes Conveying Fluid Near Critical Velocities

Journal of Applied Mechanics ◽

10.1115/1.3157760 ◽

1981 ◽

Vol 48 (4) ◽

pp. 943-947 ◽

Cited By ~ 43

Author(s):

J. Rousselet ◽

G. Herrmann

Keyword(s):

Partial Differential Equations ◽

Differential Equations ◽

Flow Velocity ◽

Averaging Method ◽

Nonlinear Partial Differential Equations ◽

Plane Motion ◽

Pipe Conveying Fluid ◽

Pipes Conveying Fluid ◽

Critical Velocities ◽

Conveying Fluid

The plane motion of a cantilevered pipe conveying fluid is examined when the flow velocity is in the neighborhood of that generating flutter. In contrast to previous studies, the flow velocity is not prescribed as a constant, but is determined from the laws of motion. We are thus led to a system of two nonlinear partial differential equations which are coupled through the nonlinear terms. The solution is found by the use of the Krylov-Bogoliubov averaging method and the results are discussed indicating the effect of nonlinearities.

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

Journal of Mechanics ◽

10.1093/jom/ufab005 ◽

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.

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Study on the Influence of Gravity Factor on Parametric Resonance of Pipe Conveying Fluid

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.300-301.1235 ◽

2013 ◽

Vol 300-301 ◽

pp. 1235-1238

Author(s):

Bing Chen ◽

Ming Le Deng ◽

Zhong Jun Yin

Keyword(s):

Flow Velocity ◽

Parametric Resonance ◽

Resonance Region ◽

Critical Conditions ◽

Pipe Conveying Fluid ◽

First Order ◽

Comparison Results ◽

Pipes Conveying Fluid ◽

The One ◽

Conveying Fluid

The averaging method has been applied to calculate the critical conditions of parametric resonance instability of the first order mode shape of clamped-clamped and pinned-pinned pipes conveying fluid. The influence of gravity factor on parametric resonance of pipe conveying fluid, with different supporting forms and different flow velocity, has been studied based on the comparison results of gravity factor being considered and neglected. It is concluded that gravity factor has a greater influence on parametric resonance region of pinned-pinned pipe than the one of clamped-clamped pipe, and, at a higher flow velocity, gravity factor is more influential to both pinned-pinned pipe and clamped- clamped one.

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