Electro-Thermo-Dynamic Buckling of Embedded DWBNNT Conveying Viscous Fluid

Document Type : Research Paper


1 Faculty of Mechanical Engineering, University of Kashan--- Institute of Nanoscience & Nanotechnology, University of Kashan

2 Institute of Nanoscience & Nanotechnology, University of Kashan


In this paper, the nonlinear dynamic buckling of double-walled boron-nitride nanotube (DWBNNT) conveying viscous fluid is investigated based on Eringen's theory. BNNT is modeled as an Euler-Bernoulli beam and is subjected to combine mechanical, electrical and thermal loading. The effect of viscosity on fluid-BNNT interaction is considered based on Navier-Stokes relation. The van der Waals (vdW) interaction between the inner and outer nanotubes is taken into account and the surrounding elastic medium is simulated as Winkler and Pasternak foundation. Considering the charge equation for coupling of mechanical and electrical fields, Hamilton's principle is utilized to derive the motion equations based on the von Kármán theory. Dynamic buckling load is evaluated using differential quadrature method (DQM). Results show that dynamic buckling load depends on small scale factor, viscosity, elastic medium parameters and temperature changes. Also, dynamic instability region is discussed for various conditions.


[1] Xu X., 2010, Dynamic torsional buckling of cylindrical shells, Computers and Structures 88: 322-330.
[2] Patel S.N., Datta P.K., Sheikh A.H., 2006, Buckling and dynamic instability analysis of stiffened shell panels, Thin-Walled Structures 44: 321-333.
[3] Païdoussis M.P., 1998, Fluid–Structure Interactions: Slender Structures and Axial Flow, Academic Press, London.
[4] Amabili M., Pellicano F., Paıïdoussis M.P., 2002, Non-linear dynamics and stability of circular cylindrical shells conveying flowing fluid, Computers and Structures 80: 899-906.
[5] Amabili M., Karagiozis K., Païdoussis M.P., 2009, Effect of geometric imperfections on non-linear stability of circular cylindrical shells conveying fluid, International Journal of Non-Linear Mechanics 44: 276-289.
[6] Karagiozis K., Amabili M., Païdoussis M.P., 2010, Nonlinear dynamics of harmonically excited circular cylindrical shells containing fluid flow, Journal of Sound and Vibration 329: 3813-3834.
[7] Païdoussis M.P., Chan S.P., Misra A.K., 1984, Dynamics and stability of coaxial cylindrical shells containing flowing fluid, Journal of Sound and Vibration 97: 201-235.
[8] Ni Q., Zhang Z.L., Wang L., 2011, Application of the differential transformation method to vibration analysis of pipes conveying fluid, Applied Mathimatics and Computation 217: 7028-7038.
[9] Yan Y., 2009, Dynamic behavior of triple-walled carbon nanotubes conveying fluid, Journal of Sound and Vibration 319: 1003-1018.
[10] Yoon J., Ru C.Q., Mioduchowski A., 2005, Vibration and instability of carbon nanotubes conveying fluid, Composite Science and Technology 65: 1326-1336.
[11] Wang L., 2009, Vibration and instability analysis of tubular nano- and micro-beams conveying fluid using nonlocal elastic theory, Physica E 41: 1835-1840.
[12] Eringen A.C., 1983, On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves, Applied Phyics 54: 4703–4710.
[13] Ke L.L., Wang Y.S., 2011, Flow-induced vibration and instability of embedded double-walled carbon nanotubes based on a modified couple stress theory, Physica E 43: 1031-1039.
[14] Ghavanloo E., Daneshmand F., Rafiei M., 2010. Vibration and instability analysis of carbon nanotubes conveying fluid and resting on a linear viscoelastic Winkler foundation, Physica E 42: 2218-2224.
[15] Khosravian N., Rafii-Tabar H., 2007. Computational modelling of the flow of viscous fluids in carbon nanotubes, Journal of Physics D: Applied Phyics 40: 7046.
[16] Wang L., Ni Q., 2009, A reappraisal of the computational modelling of carbon nanotubes conveying viscous fluid, Mechanics Resaserch Communication 36: 833-837.
[17] Salehi-Khojin A., Jalili N., 2008, Buckling of boron nitride nanotube reinforced piezoelectric polymeric composites subject to combined electro-thermo-mechanical loadings. Composite Science and Technology 68: 1489-1501.
[18] Ghorbanpour Arani A., Amir S., Shajari A.R., Mozdianfard M.R., 2012, Electro-thermo-mechanical buckling of DWBNNTs embedded in bundle of CNTs using nonlocal piezoelasticity cylindrical shell theory, Composite Part B: Engineering 43: 195-203.
[19] Mosallaie Barzoki A.A., Ghorbanpour Arani A., Kolahchi R., Mozdianfard M.R., 2012, Electro-thermo-mechanical torsional buckling of a piezoelectric polymeric cylindrical shell reinforced by DWBNNTs with an elastic core, Applied Mathimatical Modelling 36: 2983-2995.
[20] Chen L.W., Lin C.Y., Wang C.C., 2002, Dynamic stability analysis and control of a composite beam with piezoelectric layers, Composite Structures 56: 97-109.
[21] Mohammadimehr 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 24: 1289-1299.
[22] Ghorbanpour Arani A., Mosallaie Barzoki A.A., Kolahchi R., Loghman A., 2011, Pasternak foundation effect on the axial and torsional waves propagation in embedded DWCNTs using nonlocal elasticity cylindrical shell theory, Journal of Mechanical Science and Technology 25: 2385-239.
[23] Ru C.Q,., 2001, Axially compressed buckling of a doublewalled carbon nanotube embedded in an elastic medium, Journal of Mechanical Phyics and Solids 49: 1265-1279.
[24] Ghorbanpour Arani A., Hashemian M., Loghman A., Mohammadimehr M., 2011, Study of dynamic stability of the double-walled carbon nanotube under axial loading embedded in an elastic medium by the energy method, Journal of Applied Mechanic Technology and Phyics 52: 815-824.
[25] Kuang Y.D., He X.Q., Chen C.Y., Li G.Q., 2009, Analysis of nonlinear vibrations of double-walled carbon nanotubes conveying fluid, Computational Material Science 45: 875-880.
[26] Reddy J.N, 2007, Nonlocal theories for bending, buckling and vibration of beams, International Journal of Engineering and Science 45: 288-307.
[27] Yang J., 2005, AN Introduction to the theory of piezoelectricity, Springer, USA.
[28] Ke L.L., Xiang Y. , Yang J., Kitipornchai S., 2009, Nonlinear free vibration of embedded double-walled carbon nanotubes based on nonlocal Timoshenko beam theory, Computational Material Science 47: 409-417.
[29] Ansari R., Gholami R., Sahmani S., 2012, On the dynamic stability of embedded single-walled carbon nanotubes including thermal environment effects, Scientia Iranica 19: 919–925.