The surface stress effects on linear vibration of nonlocal triple-walled boron nitride nano tube conveying viscose fluid flow using DQM

Authors

Abstract

The surface stress effects on electro-thermo-mechanical linear vibration of triple-walled boron nitride nano tube embedded in an elastic medium conveying fluid flow using nonlocal Euler-Bernoulli beam theory for clamped-clamped boundary condition are investigated. The kinematic energy of fluid and nano tube, strain energy, the external work done due to the van der Waals forces, elastic medium, viscosity of fluid for nano tube, centripetal force of fluid for the inner layer of nano tube are obtained. Using energy method and applying Hamilton’s principle, the governing equations of motion for triple-walled boron nitride nano tube under surface stress effects are derived. To solve these equations, the differential quadrature method is used. Their research results show that the dimensionless natural frequency decreases with an increase in fluid velocity. Also the buckling phenomenon is occurred, when the dimensionless natural frequency is equal to zero, which the system loses its stability due to the divergence. It can be seen that the stability range increases with increasing the thickness and length to diameter due to surface stresses. This study may be useful to accurately measure the vibration characteristics of nanotubes conveying fluid flow and to design nanofluidic devices for detecting blood Glucose.

Keywords

References

1-      
[1] Eringen, A.C. (1983). “On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves”. Journal of Applied Physics, Vol. 54, pp. 4703-4710.
[2] Ghorbanpour Arani, A., Shajari, A.R., Amir, S., Loghman, A. (2012). “Electro-thermo-mechanical nonlinear nonlocal vibration and instability of embedded micro-tube reinforced by BNNT conveying fluid”. Physica E, Vol. 45, pp. 109–121.
[3] Wang, CM., Zhang, YY., He, XQ. (2007). “Vibration of nonlocal Timoshenko beams”. Nanotechnology, Vol. 18, pp. 9-18.
[4] Mohamadimehr, M., Rahmati, A.H. (2013). “Small scale effect on electro-thermo-mechanical vibration analysis of single-walled boron nitride nanorods under electric”. Turkish Journal of Engineering & Environmental Sciences, Vol. 37, pp. 1-15.
 
[5] Reddy, J.N. (2007). “Nonlocal theories for bending, buckling and vibration of beams”. International Journal of Engineering Science, Vol. 45, pp. 288–307.
[6] Mohamadimehr M., saidi, A.R., Ghorbanpour Arani, A., Arefmanesh, A., Han, Q. (2010). “Torsional buckling of a DWCNT embedded on Winkler and Pasternak foundations using nonlocal theory”. Journal of Mechanical Science and Technology, Vol. 24, pp. 1289-1299.
[7] Khodami Maraghi, Z., Ghorbanpour Arani, A., Kolahchi, R., Amir, S., Bagheri, M.R. (2013). “Nonlocal vibration and instability of embedded DWBNNT conveying viscose fluid”. Composites: Part B, Vol. 45, pp. 423–432.
[8] Wang, L. (2012). “Surface effect on buckling configuration of nanobeams containing internal flowing fluid:A nonlinear analysis”. Physica E, Vol. 44, pp. 808–812.
 [9] Gheshlaghi, B., Hasheminejad, S.M. (2011). “Surface effects on nonlinear free vibration of nanobeams”. Composites: Part B, Vol. 42, pp. 934–937.
[10] Wang, L. (2010). “Vibration analysis of fluid-conveying nanotubes with consideration of surface effects”. Physica E, Vol. 43, pp. 437–439.
[11] Samadi, F., Farshidianfar, A. (2011). “Free vibration of  carbon nanotubes conveying viscous fluid using nonlocal Timoshenko beam model”. First International Conference on Acoustics and Vibration, Amirkabir University of Tecknology, 21-22 Dec.
 [12] Kuang, YD., He, XQ., Chen, CY., Li, GQ. (2009). “Analysis of nonlinear vibrations of doublewalled carbon nanotubes conveying fluid”. Computer Material Science, Vol. 45, pp. 875–880.
[13]Reddy, JN, Wang, CM. (2004). “Dynamocs of fluid-conveying beams: governing equations and finite element models”. Singapore, Centre for Offshore Research and Engineering.
[14] Mahmoud, A.A., Awadalla, R., Nassar, M.M. (2011). “Free vibration of non-uniform column using DQM”. Mechanics Research Communication, Vol. 39, pp. 443–448.
[15] Yücel, U., Boubaker, K. (2012). “Differential quadrature method (DQM) and Boubaker Polynomials Expansion Scheme (BPES) for efficient computation of the eigenvalues of fourth-order Sturm–Liouville problems”. Applied Mathematical Modelling, Vol. 36, pp. 158–167.
[16] Haftchenari, H., Darvizeh, M., Darvizeh, A., Ansari, R., Sharma, C.B. (2007). “Dynamic analysis of composite cylindrical shells using differential quadrature method (DQM)”. Composite Structure, Vol. 78, pp. 292-298.
[17] Danesh, M., Farajpour, A., Mohammadi, M. (2012). “Axial vibration analysis of a tapered nanorod based on nonlocal elasticity theory and differential quadrature method”. Mechanics Research Communication, Vol. 39, pp. 23-27.
[18] Abdollahian, M., Ghorbanpour Arani, A., Mosallaie Barzoki, A.A., Kolahchi, R., Loghman, A. (2013). “Non-local wave propagation in embedded armchair TWBNNTs conveying viscous fluid using DQM”. Physica B, Vol. 418, pp. 1-15.
[19] Mohammadimehr, M., Saidi, A. R., Ghorbanpour Arani, A., Arefmanesh, A., Han, Q. (2011). “Buckling analysis of double-walled carbon nanotubes embedded in an elastic medium under axial compression using non-local Timoshenko beam theory”. Proceedings of the Institution of Mechanical Engineers Part C: Journal of Mechanical Engineering Science, Vol. 225, pp. 498-506.
 [20] Rahmati, A.H., Mohammadimehr, M. (2014). “Vibration analysis of non-uniform and non-homogeneous boron nitride nanorods embedded in an elastic medium under combined loadings using DQM”. Physica B, Accepted.
 
Journal of Modeling in Engineering
Volume 13, Issue 43
January 2016
Pages 47-66

Files

History

  • Receive Date: 28 January 2017
  • Revise Date: 16 September 2017
  • Accept Date: 28 January 2017

Share

How to cite

Statistics