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SCIENCE CHINA Information Sciences, Volume 64 , Issue 5 : 152201(2021) https://doi.org/10.1007/s11432-019-2822-3

Stability analysis of a pipe conveying fluid with a nonlinear energy sink

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  • ReceivedSep 27, 2019
  • AcceptedFeb 5, 2020
  • PublishedMar 15, 2021

Abstract


Acknowledgment

This work was supported by National Natural Science Foundation of China (Grant Nos. 61890920, 61890921, 61773090, 61803070), Liaoning Revitalization Talents Program (Grant No. XLYC1808015), and in part by Fundamental Research Funds for the Central Universities (Grant No. DUT19LAB37).


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  • Figure 1

    (Color online) A PCF with the NES vibration controller.

  • Figure 2

    (Color online) The energy functional, disturbance functional and Lyapunov function of PCF-NES system at different fluid velocity $v$. (a) $v=2$; (b) $v=3$.

  • Figure 3

    (Color online) The displacement response of the PCF when $v=2$. (a) Without NES; (b) with NES.

  • Figure 4

    (Color online) The displacement response of the PCF when $v=3$. (a) Without NES; (b) with NES.

  • Figure 5

    (Color online) The displacement response of the PCF and the NES at different fluid velocity $v$. (a) $v=2$; (b) $v=3$.

  • Figure 6

    (Color online) The displacement response of partial sections of the PCF at different fluid velocity $v$. protectłinebreak (a) $v=2$; (b) $v=3$.

  • Figure 7

    (Color online) The relationship between system energy $E(t)$, the total mass $\varepsilon$, and the nonlinear stiffness $k$. protectłinebreak (a) $t=1$ s; (b) $t=1.5$ s; (c) $t=2$ s; (d) $t=3$ s.

  • Table 1  

    Table 1The system parameters used in the simulation

    Parameter Description Value
    $\alpha$ The dimensionless viscoelastic coefficient of the pipe 0.001
    $\beta$ The mass ratio of the mass of fluid in the pipe and the total mass of fluid and the pipe 0.8
    $\varepsilon$ The mass ratio of the NES and the total mass of the system 0.1
    $\sigma$ The dimensionless damping of the controller 0.1
    $k$The dimensionless stiffness of the controller8000
    $d$The dimensionless installation location of the controller0.4
    $v$The dimensionless velocity of fluid in the pipe2
    $A$The initial distributed velocity in the simulation0.2