Nonlinear Forced Vibration of Cantilevered Pipes Conveying Fluid

Liu, Zhiyuan; Wang, Lin; Sun, Xiping

doi:10.1007/s10338-018-0011-0

Cited by 39 publications

(12 citation statements)

References 32 publications

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“…Moreover, the displacement amplitude inFigure 4(c) is more sensitive to frequency and becomes larger near a certain frequency. Compared with the results of Ref [40],. the numerical result in this part is verified to be correct.…”

mentioning

confidence: 80%

Shifted Legendre Polynomials algorithm used for the dynamic analysis of viscoelastic pipes conveying fluid with variable fractional order model

Wang

Chen

2020

Applied Mathematical Modelling

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The dynamic analysis of viscoelastic pipes conveying fluid is investigated with the variable fractional order model in this article. The nonlinear variable fractional order integral-differential equation is established by introducing the model into the governing equation. Then the Shifted Legendre Polynomials algorithm is first presented for dealing with this kind of equations. The numerical example verifies that the algorithm is an effective and accurate technique for addressing this type complicated equation. Numerical results for dynamic analysis of viscoelastic pipes conveying fluid show the effect of parameters on displacement, acceleration, strain and stress. It also indicates that how dynamic properties are affected by the variable fractional order and fluid velocity varying. Most of all, the proposed algorithm has enormous potentials for the problem of high precision dynamics with the variable fractional order model.

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confidence: 80%

Shifted Legendre Polynomials algorithm used for the dynamic analysis of viscoelastic pipes conveying fluid with variable fractional order model

Wang

Chen

2020

Applied Mathematical Modelling

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“…A complete dynamical model of fluid-conveying pipes involves non-linear phenomena [25,39]. However, according to author's previous research works, the non-linearity introduced by the electromagnetic force generated by the transformer devices is much more important for dynamics of a similar elastic structure with a follower force -Beck's column -than the geometrical one [38].…”

Section: Governing Equationsmentioning

confidence: 99%

Stabilization of a cantilever pipe conveying fluid using electromagnetic actuators of the transformer type

2021

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The article presents an investigation of the stabilization of a cantilever pipe discharging fluid using electromagnetic actuators of the transformer type. With the flow velocity reaching a critical value, the straight equilibrium position of the pipe becomes unstable, and self-excited lateral vibrations arise. Supplying voltage to the actuators yields two opposite effects. First, each of the actuators attracts the pipe, thus introduces the effect of negative stiffness which destabilizes the middle equilibrium. Second, lateral vibrations change the gap in magnetic circuits of the actuators, which leads to oscillations of magnetic field in the cores and the electromagnetic phenomena of induction and hysteresis that impede the motion of the pipe. The combination of these two non-linear effects is ambiguous, so the problem is explored both theoretically and experimentally. First, a mathematical model of the system in form of a partial differential equation governing the dynamics of the pipe coupled with two ordinary differential equations of electro-magnetodynamics of the actuators is presented. Then, the equation of the pipe’s dynamics is discretized using the Galerkin procedure, and the resultant set of ordinary equations is solved numerically. It has been shown that the overall effect of actuators action is positive: the critical flow velocity has been increased and the amplitude of post-critical vibrations reduced. These results have been validated experimentally on a test stand.

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“…Te pseudoarclength continuation technique along with direct time integration is used to solve these equations. Liu et al [8] explored the nonlinear forced vibrations of a cantilevered pipe conveying fuid under base excitations by means of the full nonlinear equation of motion. Te self-excited vibration is briefy discussed, focusing on the efect of fow velocity on the stability and postfutter dynamical behavior of the pipe system with parameters close to those in previous experiments.…”

Section: Introductionmentioning

confidence: 99%

Hopf Bifurcation of a Standing Cantilever Pipe Conveying Fluid with Time Delay

Cao

Ou³

2022

Mathematical Problems in Engineering

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In this article, the dynamical behavior of a standing cantilever pipe conveying fluid is investigated with time − delay. By applying piezoelectric materials and considering the time delay of voltage, the motion equation is built with motion-limiting constraints and elastic support. The motion equation is discretized into ordinary differential equations by the Galerkin method. A stability analysis of the equilibrium point with three parameters is obtained. The system will lose stability at the equilibrium point and generate Hopf branches. The central manifold theorem and the canonical type theory are used to study the stability of Hopf branching directions and branching period solutions. Finally, numerical results validate the theoretical analysis.

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Nonlinear Forced Vibration of Cantilevered Pipes Conveying Fluid

Cited by 39 publications

References 32 publications

Shifted Legendre Polynomials algorithm used for the dynamic analysis of viscoelastic pipes conveying fluid with variable fractional order model

Shifted Legendre Polynomials algorithm used for the dynamic analysis of viscoelastic pipes conveying fluid with variable fractional order model

Stabilization of a cantilever pipe conveying fluid using electromagnetic actuators of the transformer type

Hopf Bifurcation of a Standing Cantilever Pipe Conveying Fluid with Time Delay

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