Hostname: page-component-cd9895bd7-jn8rn Total loading time: 0 Render date: 2024-12-25T17:27:19.116Z Has data issue: false hasContentIssue false
  • English
  • Français

Dynamics and Stability of Pinned-Free Micropipes Conveying Fluid

Published online by Cambridge University Press:  25 May 2017

K. Hu ,
H. L. Dai ,
L. Wang  and
Q. Qian
K. Hu
Affiliation:
Department of MechanicsHuazhong University of Science and TechnologyWuhan, China
H. L. Dai
Affiliation:
Department of MechanicsHuazhong University of Science and TechnologyWuhan, China
L. Wang*
Affiliation:
Department of MechanicsHuazhong University of Science and TechnologyWuhan, China
Q. Qian
Affiliation:
Department of MechanicsHuazhong University of Science and TechnologyWuhan, China
*
*Corresponding author ([email protected])
Get access

Abstract

In this paper, the dynamical behavior and stability of hanging micropipes conveying fluid with pinned-free boundary conditions are investigated. For a pinned-free rigid micropipe, the dynamical system is found to be stable for various flow velocities. Particular emphasis is placed on the effects of flow velocity, mass ratio and gravity on the dynamics and flutter instability of flexible micropipe system with pinned-free boundary conditions. The governing equations for flexible micropipes are discretized using the differential quadrature method (DQM), yielding a generalized eigenvalue problem which is then solved for various flow velocities, mass ratios and gravity parameters. It is shown that, with increasing flow velocity, the flexible micropipe with pinned-free boundary conditions is stable until it becomes unstable via a Hopf bifurcation leading to flutter. The system may lose stability first in the second or third mode, mainly depending on the selected value of mass ratio. The existence of mode exchange between the second and third modes is possible. The gravity parameter of positive values causes additional restoring force and hence enhances the stability of the micropipe system; however, it can generate the complexity of stability diagrams.

Keywords

Micropipe conveying fluidDynamicsStabilityFlutter
Type
Research Article
Information
Journal of Mechanics , Volume 34 , Issue 4 , August 2018 , pp. 533 - 539
Copyright
Copyright © The Society of Theoretical and Applied Mechanics 2018 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1. Rinaldi, S., Prabhakar, S., Vengallator, S. and Paidoussis, M. P., “Dynamics of Microscale Pipes Containing Internal Fluid Flow: Damping, Frequency Shift, and Stability,” Journal of Sound and Vibration, 329, pp. 1081–1088 (2010).Google Scholar
2. Wang, L., Hong, Y. Z., Dai, H. L. and Ni, Q., “Natural Frequency and Stability Tuning of Cantilevered CNTs Conveying Fluid in Magnetic Field,” Acta Mechanica Solida Sinica, 29, pp. 567–576 (2016).Google Scholar
3. Zhang, W. M. et al., “Dynamics of Suspended Microchannel Resonators Conveying Opposite Internal Fluid Flow: Stability, Frequency Shift and Energy Dissipation,” Journal of Sound and Vibration, 368, pp. 103–120 (2016).Google Scholar
4. Olcum, S., Cermak, N., Wasserman, S. C. and Manalis, S. R., “High-Speed Multiple-Mode Mass-Sensing Resolves Dynamic Nanoscale Mass Distributions,” Nature Communications, 6, 7070 (2015)Google Scholar
5. Chaste, J. et al., “A Nanomechanical Mass Sensor with Yoctogram Resolution,” Nature Nanotechnology, 7, pp. 301–304 (2012).Google Scholar
6. Hanay, M. S. et al., “Single-Protein Nanomechanical Mass Spectrometry in Real Time,” Nature Nanotechnology, 7, pp. 602–608 (2012).Google Scholar
7. Chang, T.-P., “Thermal-Nonlocal Vibration and Instability of Single-Walled Carbon Nanotubes Conveying Fluid,” Journal of Mechanics, 27, pp. 567–573 (2011).Google Scholar
8. Burg, T. P. et al., “Weighing of Biomolecules Single Cells and Single Nanoparticles in Fluid,” Nature, 446, pp. 1066–1069 (2007).Google Scholar
9. Wang, B., Deng, Z. C., Ouyang, H. J. and Xu, X. J., “Free Vibration of Wavy Single-Walled Fluid-Conveying Carbon Nanotubes in Multi-Physics Fields,” Applied Mathematical Modelling, 39, pp. 6780–6792(2015).Google Scholar
10. Liang, F. and Su, Y., “Stability Analysis of a Single-Walled Carbon Nanotubes Conveying Pulsating and Viscous Fluid with Nonlocal Effect,” Applied Mathematical Modelling, 37, pp. 6821–6828 (2013).Google Scholar
11. Wang, L. F., Guo, W. L. and Hu, H. Y., “Flexural Wave Dispersion in Multi-Walled Carbon Nanotubes Conveying Fluids,” Acta Mechanica Solida Sinica, 22, pp. 623–629 (2009).Google Scholar
12. Zhang, Z. J., Liu, Y. S., Zhao, H. L. and Liu, W., “Acoustic Nanowave Absorption through Clustered Carbon Nanotubes Conveying Fluid,” Acta Mechanica Solida Sinica, 29, pp. 257–270 (2016).Google Scholar
13. Deng, Q. T. and Yang, Z. C., “Vibration of Fluid-Filled Multi-Walled Carbon Nanotubes Seen via Nonlocal Elasticity Theory,” Acta Mechanica Solida Sinica, 27, pp. 568–578 (2014).Google Scholar
14. Paidoussis, M. P., Luu, T. P. and Prabhakar, S., “Dynamics of a Long Tubular Cantilever Conveying Fluid Downwards, which Then Flows Upwards around the Cantilever as a Confined Annular Flow,” Journal of Fluids and Structures, 24, pp. 111–128 (2008).Google Scholar
15. Lam, D. C. C., Yang, F., Chong, A. C. M., Wang, J. and Tong, P., “Experiments and Theory in Strain Gradient Elasticity,” Journal of the Mechanics and Physics of Solids, 51, pp. 1477–1508(2003).Google Scholar
16. Liu, D. B. et al., “Toward a Further Understanding of Size Effects in the Torsion of Thin Metal Wires: An Experimental and Theoretical Assessment,” International Journal of Plasticity, 41, pp. 30–52 (2013).Google Scholar
17. Liu, D. B. et al., “Size Effects in the Torsion of Microscale Copper Wires: Experiment and Analysis,” Scripta Materialia, 66, pp. 406–409 (2012).Google Scholar
18. Yang, F., Chong, A. C. M., Lam, D. C. C. and Tong, P., “Couple Stress Based Strain Gradient Theory for Elasticity,” International Journal of Solids and Structures, 39, pp. 2731–2743 (2002).Google Scholar
19. Wang, B., Zhao, J. and Zhou, S., “A Micro Scale Timoshenko Beam Model Based on Strain Gradient Elasticity Theory,” European Journal of Mechanics-A/Solids, 29, pp. 591–599 (2010).Google Scholar
20. Wang, L., “Size-Dependent Vibration Characteristics of Fluid-Conveying Microtubes,” Journal of Fluids and Structures, 26, pp. 675–684 (2010).Google Scholar
21. Wang, L., Liu, H. T., Ni, Q. and Wu, Y., “Flexural Vibrations of Microscale Pipes Conveying Fluid by Considering the Size Effects of Micro-Flow and Micro-Structure,” International Journal of Engineering Science, 71, pp. 92–101 (2013).Google Scholar
22. Setoodeh, A. and Afrahim, S., “Nonlinear Dynamic Analysis of FG Micro-Pipes Conveying Fluid Based on Strain Gradient Theory,” Composite Structures, 116, pp. 128–135 (2014).Google Scholar
23. Hosseini, M. and Bahaadini, R., “Size Dependent Stability Analysis of Cantilever Micro-Pipes Conveying Fluid Based on Modified Couple Strain Gradient Theory,” International Journal of Engineering Science, 101, pp. 1–13 (2016).Google Scholar
24. Dai, H. L., Wang, L. and Ni, Q., “Dynamics and Pull-in Instability of Electrostatically Actuated Microbeams Conveying Fluid,” Microfluidics and Nanofluidics, 18, pp. 49–55 (2015).Google Scholar
25. Yan, H. et al., “Dynamical Characteristics of Fluid-Conveying Microbeams Actuated by Electrostatic Force,” Microfluidics and Nanofluidics, 20, 137 (2016).Google Scholar
26. Yang, T. Z., Ji, S., Yang, X. D. and Fang, B., “Microfluid-Induced Nonlinear Free Vibration of Microtubes,” International Journal of Engineering Science, 76, pp. 47–55 (2014).Google Scholar
27. Mashroutech, S., Sadri, M., Younesian, D. and Esmailzadeh, E., “Nonlinear Vibration Analysis of Fluid-Conveying Microtubes,” Nonlinear Dynamics, 85, pp. 1007–1021 (2016).Google Scholar
28. Hu, K., Wang, Y. K., Dai, H. L., Wang, L. and Qian, Q., “Nonlinear and Chaotic Vibrations of Cantilevered Micropipes Conveying Fluid Based on Modified Couple Stress Theory,” International Journal of Engineering Science, 105, pp. 93–107 (2016).Google Scholar
29. Guo, C. Q., Zhang, C. H. and Païdoussis, M. P., “Modification of Equation of Motion of Fluid-Conveying Pipe for Laminar and Turbulent Flow Profiles,” Journal of Fluids and Structures, 26, pp. 793–803 (2010).Google Scholar
30. Benjamin, T. B., “Dynamics of a System of Articulated Pipes Conveying Fluid. I. Theory,” Proceedings of the Royal Society (London) A, 261, pp. 457–486 (1961).Google Scholar
31. Ansari, R., Gholami, R. and Shahabodini, A., “Size-Dependent Geometrically Nonlinear Forced Vibration Analysis of Functionally Graded First-Order Shear Deformable Microplates,” Journal of Mechanics, 32, pp. 539–554 (2016).Google Scholar
32. Kheiri, M., Paidoussis, M. P., Costa Del Pozo, G. and Amabili, M., “Dynamics of a Pipe Conveying Fluid Flexibly Restrained at the Ends,” Journal of Fluids and Structures, 49, pp. 360–385 (2014).Google Scholar