Microsystem Technologies

, Volume 25, Issue 1, pp 197–210 | Cite as

Vibration analysis of suspended microchannel resonators characterized as cantilevered micropipes conveying fluid and nanoparticle

  • Ke Hu
  • Pan Wu
  • Lin Wang
  • Hu-Liang Dai
  • Qin Qian
Technical Paper


This paper performs a theoretical analysis of suspended microchannel resonators (SMRs) containing one single or two parallel channels, modeled here as cantilevered micropipes conveying fluid and nanoparticle, and investigates the effects of flow velocity and nanoparticle’s instantaneous position on natural frequency, stability, and damping. For two-channel micropipes (TCMPs), the governing equation is derived using the Newtonian approach by essentially accounting for the flow-induced tensile force due to the fact that the flow reverses direction near the free end of the micropipe. Results of eigenvalue analysis show that the presence of a moving nanoparticle can make originally stable micropipe systems become unstable. The stability of both single-channel micropipes (SCMPs) and TCMPs is strongly dependent on the instantaneous position of the moving nanoparticle. For a TCMP system, of particular interest is that in the absence of external damping, flutter instability may concurrently occurs in several modes even for infinitesimal flow velocity. The same TCMP system but with consideration of external damping, however, can retain stability at low flow velocity. These results highlight the importance of considering fluid–structure interactions in the design of SMRs containing internal flow and nanoparticle.



The authors gratefully acknowledge the support provided by the National Natural Science Foundation of China (Nos. 11622216 and 11572133).


  1. Abbasnejad B, Shabani R, Rezazadeh G (2015) Stability analysis of a piezoelectrically actuated micro-pipe conveying fluid. Microfluid Nanofluid 19:577–584CrossRefGoogle Scholar
  2. Afkhami Z, Farid M (2016) Thermo-mechanical vibration and instability of carbon nanocones conveying fluid using nonlocal Timoshenko beam model. J Vib Control 22:604–618MathSciNetCrossRefGoogle Scholar
  3. Amiri A, Pournaki IJ, Jafarzadeh E, Shabani R, Rezazadeh G (2016) Vibration and instability of fluid-conveyed smart micro-tubes based on magneto-electro-elasticity beam model. Microfluid Nanofluid 20:38CrossRefGoogle Scholar
  4. Ansari R, Norouzzadeh A, Gholami R, Shojaei MF, Darabi MA (2016) Geometrically nonlinear free vibration and instability of fluid-conveying nanoscale pipes including surface stress effects. Microfluid Nanofluid 20:28CrossRefGoogle Scholar
  5. Bargatin I, Myers EB, Aldridge JS, Marcoux C, Brianceau P, Duraffourg L, Coline E, Hentz S, Andreucci P, Roukes ML (2012) Large-scale integration of nanoelectromechanical systems for gas sensing applications. Nano Lett 12:1269–1274CrossRefGoogle Scholar
  6. Burg TP, Godin M, Knudsen SM, Shen W, Carlson G, Foster JS, Babcock K, Manalis SR (2007) Weighing of biomolecules single cells and single nanoparticles in fluid. Nature 446:1066–1069CrossRefGoogle Scholar
  7. Chang TP (2013) Nonlinear thermal-mechanical vibration of flow-conveying double-walled carbon nanotubes subjected to random material property. Microfluid Nanofluid 15:219–229CrossRefGoogle Scholar
  8. Chaste J, Eichler A, Moser J, Ceballos G, Rurali R, Bachtold A (2012) A nanomechanical mass sensor with yoctogram resolution. Nat Nanotechnol 7:301–304CrossRefGoogle Scholar
  9. Dai HL, Wang L, Ni Q (2015a) Dynamics and pull-in instability of electrostatically actuated microbeams conveying fluid. Microfluid Nanofluid 18:49–55CrossRefGoogle Scholar
  10. Dai HL, Wang YK, Wang L (2015b) Nonlinear dynamics of cantilevered microbeams based on modified couple stress theory. Int J Eng Sci 94:103–112MathSciNetCrossRefzbMATHGoogle Scholar
  11. Farokhi H, Ghayesh MH, Hussain S (2016) Large-amplitude dynamical behaviour of microcantilevers. Int J Eng Sci 106:29–41CrossRefzbMATHGoogle Scholar
  12. Fazelzadeh SA, Kazemi-Lari MA (2013) Stability analysis of partially loaded Leipholz column carrying a lumped mass and resting on elastic foundation. J Sound Vib 332:595–607CrossRefGoogle Scholar
  13. Godin M, Delgado FF, Son S, Grover WH, Bryan AK, Tzur A, Jorgensen P, Payer K, Grossman AD, Kirschner MW, Manalis SR (2010) Using buoyant mass to measure the growth of single cells. Nat Methods 7:387–390CrossRefGoogle Scholar
  14. Gregory RW, Paidoussis MP (1966) Unstable oscillation of tubular cantilevers conveying fluid. I. Theory. Proc R Soc A 293:512–527zbMATHGoogle Scholar
  15. Grover WH, Bryan AK, Diez-Silva M, Suresh S, Higgins JM, Manalis SR (2010) Measuring single-cell density. Proc Natl Acad Sci USA 108:10992–10996CrossRefGoogle Scholar
  16. Guo CQ, Zhang CH, Païdoussis MP (2010) Modification of equation of motion of fluid-conveying pipe for laminar and turbulent flow profiles. J Fluids Struct 26:793–803CrossRefGoogle Scholar
  17. Hanay MS, Kelber S, Naik AK, Chi D, Hentz S, Bullard EC, Colinet E, Duraffourg L, Roukes ML (2012) Single-protein nanomechanical mass spectrometry in real time. Nat Nanotechnol 7:602–608CrossRefGoogle Scholar
  18. Hosseini M, Bahaadini R (2016) Size dependent stability analysis of cantilever micro-pipes conveying fluid based on modified couple strain gradient theory. Int J Eng Sci 101:1–13CrossRefzbMATHGoogle Scholar
  19. Hu K, Wang YK, Dai HL, Wang L, Qian Q (2016) Nonlinear and chaotic vibrations of cantilevered micropipes conveying fluid based on modified couple stress theory. Int J Eng Sci 105:93–107MathSciNetCrossRefzbMATHGoogle Scholar
  20. Karami H, Farid M (2015) A new formulation to study in-plane vibration of curved carbon nanotubes conveying viscous fluid. J Vib Control 21:2360–2371MathSciNetCrossRefGoogle Scholar
  21. Kazemi-Lari MA, Fazelzadeh SA, Ghavanloo E (2012) Non-conservative instability of cantilever carbon nanotubes resting on viscoelastic foundation. Phys E 44:1623–1630CrossRefGoogle Scholar
  22. Ke LL, Wang YS (2011) Flow-induced vibration and instability of embedded double-walled carbon nanotubes based on a modified couple stress theory. Phys E 43:1031–1039CrossRefGoogle Scholar
  23. Kong LC, Xie X, Zhang J, Wang YX, Hu YT (2015) On the interaction between a quartz crystal resonator and an array of micro-beams in thickness-shear vibrations. Acta Mech Solida Sin 28:464–470CrossRefGoogle Scholar
  24. Kuang YD, Shi SQ (2014) Strong mechanical coupling between the carbon nanotube and the inner streaming water flow. Microfluid Nanofluid 17:1053–1060CrossRefGoogle Scholar
  25. Lam DCC, Yang F, Chong ACM, Wang J, Tong P (2003) Experiments and theory in strain gradient elasticity. J Mech Phys Solids 51:1477–1508CrossRefzbMATHGoogle Scholar
  26. Lee J, Shen W, Payer K, Burg TP, Manalis SR (2010) Toward attogram mass measurements in solution with suspended nanochannel resonators. Nano Lett 10:2537–2542CrossRefGoogle Scholar
  27. Li M, Tang HX, Roukes ML (2007) Ultra-sensitive NEMS-based cantilevers for sensing, scanned probe and very high-frequency applications. Nat Nanotechnol 2:114–120CrossRefGoogle Scholar
  28. Li L, Hu YJ, Li XB, Ling L (2016) Size -dependent effects on critical flow velocity of fluid-conveying microtubes via nonlocal strain gradient theory. Microfluid Nanofluid 20:76CrossRefGoogle Scholar
  29. Liu ZY, Wang L, Sun XP (2018) Nonlinear forced vibration of cantilevered pipes conveying fluid. Acta Mech Solida Sin 31:32–50CrossRefGoogle Scholar
  30. Liu DB, He YM, Tang XT, Ding HM, Hu P, Cao P (2012) Size effects in the torsion of microscale copper wires: experiment and analysis. Scr Mater 66:406–409CrossRefGoogle Scholar
  31. Liu DB, He YM, Dunstan DJ, Zhang B, Gan ZP, Hu P, Ding HM (2013) Toward a further understanding of size effects in the torsion of thin metal wires: an experimental and theoretical assessment. Int J Plast 41:30–52CrossRefGoogle Scholar
  32. Mashroutech S, Sadri M, Younesian D, Esmailzadeh E (2016) Nonlinear vibration analysis of fluid-conveying microtubes. Nonlinear Dyn. MathSciNetGoogle Scholar
  33. Olcum S, Cermak N, Wasserman SC, Christine KS, Atsumi H, Payer KR, Shen WJ, Lee JC, Belcher AM, Bhatia SN, Manalis SR (2014) Weighing nanoparticles in solution at the attogram scale. Proc Natl Acad Sci USA 111:1310–1315CrossRefGoogle Scholar
  34. Olcum S, Cermak N, Wasserman SC, Manalis SR (2015) High-speed multiple-mode mass-sensing resolves dynamic nanoscale mass distributions. Nat Commun 6:7070CrossRefGoogle Scholar
  35. Paidoussis MP (1998) Fluid-structure interactions: slender structures and axial flow, vol 1. Academic Press, LondonGoogle Scholar
  36. Park K, Millet LJ, Kim N, Li H, Jin XZ, Popescu G, Aluru NR, Hsia KJ, Bashir R (2010) Measurement of adherent cell mass and growth. Proc Natl Acad Sci USA 107:20691–20696CrossRefGoogle Scholar
  37. Rinaldi S, Prabhakar S, Vengallator S, Paidoussis MP (2010) Dynamics of microscale pipes containing internal fluid flow: damping, frequency shift, and stability. J Sound Vib 329:1081–1088CrossRefGoogle Scholar
  38. Setoodeh A, Afrahim S (2014) Nonlinear dynamic analysis of FG micro-pipes conveying fluid based on strain gradient theory. Compos Struct 116:128–135CrossRefGoogle Scholar
  39. Tang Y, Yang TZ, Fang B (2018) Fractional dynamics of fluid-conveying pipes made of polymer-like materials. Acta Mech Solida Sin 31:243–258CrossRefGoogle Scholar
  40. Wang L, Liu HT, Ni Q, Wu Y (2013) Flexural vibrations of microscale pipes conveying fluid by considering the size effects of micro-flow and micro-structure. Int J Eng Sci 71:92–101MathSciNetCrossRefzbMATHGoogle Scholar
  41. Wang L, Hong YZ, Dai HL, Ni Q (2016) Natural frequency and stability tuning of cantilevered CNTs conveying fluid in magnetic field. Acta Mech Solida Sin 29:567–576CrossRefGoogle Scholar
  42. Yang F, Chong ACM, Lam DCC, Tong P (2002) Couple stress based strain gradient theory for elasticity. Int J Solids Struct 39:2731–2743CrossRefzbMATHGoogle Scholar
  43. Yang TZ, Ji S, Yang XD, Fang B (2014) Microfluid-induced nonlinear free vibration of microtubes. Int J Eng Sci 76:47–55CrossRefzbMATHGoogle Scholar
  44. Zhang ZJ, Liu YS, Zhao HL, Liu W (2016a) Acoustic nanowave absorption through clustered carbon nanotubes conveying fluid. Acta Mech Solida Sin 29:257–270CrossRefGoogle Scholar
  45. Zhang WM, Yan H, Jiang HM, Hu KM, Peng ZK, Meng G (2016b) Dynamics of suspended microchannel resonators conveying opposite internal fluid flow: stability, frequency shift and energy dissipation. J Sound Vib 368:103–120CrossRefGoogle Scholar
  46. Zhang YW, Zhou L, Fang B, Yang TZ (2017) Quantum effects on thermal vibration of single-walled carbon nanotubes conveying fluid. Acta Mech Solida Sin 30:550–556CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Ke Hu
    • 1
    • 2
  • Pan Wu
    • 1
    • 2
  • Lin Wang
    • 1
    • 2
  • Hu-Liang Dai
    • 1
    • 2
  • Qin Qian
    • 1
    • 2
  1. 1.Department of Mechanics, College of Civil Engineering and MechanicsHuazhong University of Science and TechnologyWuhanChina
  2. 2.Hubei Key Laboratory for Engineering Structural Analysis and Safety AssessmentWuhanChina

Personalised recommendations