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A study on the dynamic instabilities of a smart embedded micro-shell induced by a pulsating flow: A nonlocal piezoelastic approach

  • Atabakhshian, Vahid (Department of Mechanical Engineering, Faculty of Engineering, Bu-Ali Sina University) ;
  • Shooshtaria, Alireza (Department of Mechanical Engineering, Faculty of Engineering, Bu-Ali Sina University)
  • Received : 2018.01.30
  • Accepted : 2020.04.14
  • Published : 2020.10.25
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Abstract

In this study, nonlinear vibrations and dynamic instabilities of a smart embedded micro shell conveying varied fluid flow and subjected to the combined electro-thermo-mechanical loadings are investigated. With the aim of designing new hydraulic sensors and actuators, the piezoelectric materials are employed for the body and the effects of applying electric field on the stability of the system as well as the induced voltage due to the dynamic behavior of the system are studied. The nonlocal piezoelasticity theory and the nonlinear cylindrical shell model in conjunction with the energy approach are utilized to mathematically modeling of the structure. The fluid flow is assumed to be isentropic, incompressible and fully develop, and for more generality of the problem both steady and time dependent flow regimes are considered. The mathematical modeling of fluid flow is also carried out based on a scalar potential function, time mean Navier-Stokes equations and the theory of slip boundary condition. Employing the modified Lagrange equations for open systems, the nonlinear coupled governing equations of motion are achieved and solved via the state space problem; forth order numerical integration and Bolotin's method. In the numerical results, a comprehensive discussion is made on the dynamical instabilities of the system (such as divergence, flutter and parametric resonance). We found that applying positive electric potential field will improve the stability of the system as an actuator or vibration amplitude controller in the micro electro mechanical systems.

Keywords

References

  1. Alinia, M.M. and Ghannadpour, S. (2009), "Nonlinear analysis of pressure loaded FGM plates", Compos. Struct., 88(3), 354-359. https://doi.org/10.1016/j.compstruct.2008.04.013.
  2. Amabili, M. (2008), Nonlinear Vibrations and Stability of Shells and Plates, Cambridge University Press, Parma, Italy.
  3. Arani, A.G., Shajari, A.R., Amir, S. and Atabakhshian, V. (2013a), "Nonlinear fluid-induced vibration and instability of an embedded piezoelectric polymeric microtube using nonlocal elasticity theory", J. Mech. Eng. Sci., 227(12), 2870-2885. https://doi.org/10.1177/0954406213479094.
  4. Arani, A.G., Shajari, A.R., Atabakhshian, V., Amir, S. and Loghman, A. (2013b), "Nonlinear dynamical response of embedded fluid-conveyed micro-tube reinforced by BNNTs", Compos. Part B Eng., 44(1), 424-432. https://doi.org/10.1016/j.compositesb.2012.04.025.
  5. Ashley, H. and Haviland, G. (1950), "Bending vibrations of a pipeline containing flowing fluid", J. Appl. Mech., 72, 229-232. https://doi.org/10.1115/1.4010122
  6. Atabakhshian, V., Shoshtari, A.R. and Karimi, M. (2015), "Electro-thermal vibration of a smart coupled nanobeam system with an internal flow based on nonlocal elasticity theory", Physica B Condens. Matter, 456, 375-382. https://doi.org/10.1016/j.physb.2014.08.043.
  7. Azrar, A., Azrar, L. and Aljinaidi, A.A. (2015), "Numerical modeling of dynamic and parametric instabilities of single-walled carbon nanotubes conveying pulsating and viscous fluid", Compos. Struct., 125(8), 127-143. https://doi.org/10.1016/j.compstruct.2015.01.044.
  8. Bolotin, V.V. (1964), The Dynamic Stability of Elastic Systems, Holden-Day, San Francisco, USA.
  9. Da, H.L., Wang, L., Qian, Q. and Ni, Q. (2014), "Vortex-induced vibrations of pipes conveying pulsating fluid", Ocean Eng., 77, 12-22. https://doi.org/10.1016/j.oceaneng.2013.12.006.
  10. Dharap, P., Li, Z., Nagarajaiah, S. and Barrera, E.V. (2004), "Nanotube film based on single-wall carbon nanotubes for strain sensing", Nanotechnology, 15(3), 379. https://doi.org/10.1088/0957-4484/15/3/026.
  11. Ding, H.J. and Chen, W.Q. (2001), Three Dimensional Problems of Piezoelasticity, Nova Science, New York, USA.
  12. Eringen, C. (1983), "On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves", J. Appl. Phys., 54, 4703-4710. https://doi.org/10.1063/1.332803.
  13. Fox, R.W., Pritchard, P.J. and McDonald, A.T. (2008), Introduction to Fluid Mechanics, Wiley, New York, USA.
  14. Gao, J. and Xu, B. (2009), "Applications of nanomaterials inside cells", Nano Today, 4(1), 37-51. https://doi.org/10.1016/j.nantod.2008.10.009.
  15. Gu, J., Ma, T. and Menglan, D. (2016), "Effect of aspect ratio on the dynamic response of a fluid-conveying pipe using the Timoshenko beam model", Ocean Eng., 114, 185-191. https://doi.org/10.1016/j.oceaneng.2016.01.021.
  16. IEEE Standard (1978), IEEE Standard on Piezoelectricity, IEEE, New York, USA.
  17. Karniadakis, G., Beskok, A. and Aluru, N. (2005), Micro Flows Nano Flows: Fundamentals and Simulation, Springer-Verlag, USA.
  18. Kamm, R.D. and Pedley, T.J. (1989), "Flow in collapsible tubes: A brief review", J. Biomech. Eng., 111, 177-179. https://doi.org/10.1115/1.3168362.
  19. Kong, J., Franklin, N.R., Zhou, C., Chapline, M.G., Peng, S., Cho, K. and Dai, H. (2000), "Nanotube molecular wires as chemical sensors", Science, 287(5453), 622-625. https://doi.org/10.1126/science.287.5453.622.
  20. Kuang, Y.D., He, X.Q., Chen, C.Y. and Li, G.Q. (2009), "Analysis of nonlinear vibrations of double-walled carbon nanotubes conveying fluid", Int. J. Comput. Mater. Sci. Surf. Eng., 45, 875-880. https://doi.org/10.1016/j.commatsci.2008.12.007.
  21. Kurylov, Y. and Amabili, M. (2010), "Polynomial versus trigonometric expansions for nonlinear vibrations of circular cylindrical shells with different boundary conditions", J. Sound Vib., 329(9), 1435-1449. https://doi.org/10.1016/j.jsv.2009.10.038.
  22. Liang, F. and Su, Y. (2013), "Stability analysis of a single-walled carbon nanotube conveying pulsating and viscous fluid with nonlocal effect", Appl. Math. Model., 37, 6821-6828. https://doi.org/10.1016/j.apm.2013.01.053.
  23. Paidoussis, M.P. (1998), Fluid-Structure Interactions: Slender Structures and Axial Flow Volume 1, Academic Press, London, UK.
  24. Paidoussis, M.P. (2003), Fluid-Structure Interactions: Slender Structures and Axial Flow, Volume 2, Academic press, London, UK.
  25. Paidoussis, M.P., Misra, A.K. and Chan, S.P. (1985), "Dynamics and stability of coaxial cylindrical shells conveying viscous fluid", J. Appl. Mech. Trans., 52(2), 389-396. https://doi.org/10.1016/0022-460X(84)90319-5.
  26. Panda, L.N. and Kar, R.C. (2008), "Nonlinear dynamics of a pipe conveying pulsating fluid with combination, principal parametric and internal resonances", 309, 375-406. https://doi.org/10.1016/j.jsv.2007.05.023.
  27. Pellicano, F. and Amabili, M. (2006), "Dynamic instability and chaos of empty and fluid-filled circular cylindrical shells under periodic axial loads", J. Sound Vib., 293, 227-252. https://doi.org/10.1016/j.jsv.2005.09.032.
  28. Rashidi, V., Mirdamadi, H.R. and Shirani, E. (2012), "A novel model for vibrations of nanotubes conveying nanoflow", Comput. Mater. Sci., 51, 347-352. https://doi.org/10.1016/j.commatsci.2011.07.030.
  29. Reddy, J.N. and Wang, C.M. (2004), "Dynamics of fluid conveying beams: Governing equations and finite element models", CORE Report No. 2004-03, Centre for Offshore Research and Engineering National University of Singapore, Singapore.
  30. Sadeghi, M.H. and Karimi-Dona, M.H. (2011), "Dynamic behavior of a fluid conveying pipe subjected to a moving sprung mass: an FEM-state space approach", Int. J. Press. Vessels Pip. 88(4), 123-131. https://doi.org/10.1016/j.ijpvp.2011.02.004.
  31. Shokouhmand, H., Isfahani, A.H.M. and Shirani, E. (2010), "Friction and heat transfer coefficient in micro and nano channels filled with potous media for wide range of Knudsen number", Int. Comm. Heat Mass Transfer, 37, 890-894. https://doi.org/10.1016/j.icheatmasstransfer.2010.04.008.
  32. Tubaldi, E., Amabili, V. and Paidoussis, M.P. (2016), "Fluidstructure interaction for nonlinear response of shells conveying pulsatile flow", J. Sound Vib., 371, 252-276. https://doi.org/10.1016/j.jsv.2016.01.024
  33. Tubaldi, E., Amabili, M. and Paidoussis, M.P. (2017), "Nonlinear dynamics of shells conveying pulsatile flow with pulse-wave propagation: Theory and numerical results for a single harmonic pulsation", J. Sound Vib., 396, 217-245. https://doi.org/10.1016/j.jsv.2017.01.044.
  34. Wang, L. (2009), "A further study on the non-linear dynamics of simply supported pipes conveying pulsating fluid", Int. J. Nonlinear Mech., 44, 115-121. https://doi.org/10.1016/j.ijnonlinmec.2008.08.010.
  35. Yan, Y., Wang, W.Q. and Zhang, L.X. (2009), "Dynamical behaviors of fluid-conveyed multi walled carbon nanotubes", Appl. Math. Model., 33, 1430-1440. https://doi.org/10.1016/j.apm.2008.02.010.
  36. Yang, J. (2005), An Introduction to the Theory of Piezoelectricity, Springer, Lincoln, USA.
  37. Yang, J., Ke, L.L. and Kitipornchai, S. (2010), "Nonlinear free vibration of single-walled carbon nanotubes using nonlocal Timoshenko beam theory", Physica E Low Dimens. Syst. Nanostruct., 42, 1727-1735. https://doi.org/10.1016/j.physe.2010.01.035.
  38. Yang, K.S., Cheng, Y.C., Liu, M.C. and Shyu, J.C. (2015), "Micro pulsating heat pipes with alternate microchannel widths", Appl. Therm. Eng., 83, 131-138. https://doi.org/10.1016/j.applthermaleng.2015.03.020.