Nonlocal Vibration of Y-SWCNT Conveying Fluid Considering a General Nonlocal Elastic Medium

Document Type: Research Paper


1 School of Mechanical Engineering, College of Engineering, University of Tehran, Tehran, Iran

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

3 Faculty of Mechanical Engineering, University of Kashan, Kashan, Iran


In this paper, a nonlocal foundation model is proposed to analyze the vibration and instability of a Y-shaped single-walled carbon nanotube (Y-SWCNT) conveying fluid. In order to achieve more accurate results, fourth order beam theory is utilized to obtain strain-displacement relations. For the first time, a nonlocal model is presented based on nonlocal elasticity and the effects of nonlocal forces from adjacent and non-adjacent elements on deflection are considered. The Eringen’s theory is utilized due to its capability to consider the size effect. Based on Hamilton’s principle, motion equations as well as boundary conditions are derived and solved by means of hybrid analytical-numerical method. It is believed that the presented general foundation model offers an exact and effective new approach to investigate vibration characteristics of this kind of structures embedded in an elastic medium. The results of this investigation may provide a useful reference in controlling systems in nano-scale.


[1] Terrones M., Banhart F., Grobert N., Charlier J.C., Terrones H., Ajayan P., 2002, Molecular junctions by joining single-walled carbon nanotubes, Physical Review Letters 89: 075505.
[2] Andriotis A., Menon M., Srivastava D., Chernozatonskii L., 2001, Rectification properties of carbon nanotube Y-junctions, Physical Review Letters 87: 066802.
[3] Papadopoulos C., Rakitin A, Li J., Vedeneev A., Xu J., 2000, Electronic transport in Y-junction carbon nanotubes, Physical Review Letters 85(16): 3476.
[4] Bandaru P., Daraio C., Jin S., Rao A., 2005, Novel electrical switching behaviour and logic in carbon nanotube Y-junctions, Nature Materials 4: 663-668.
[5] Sattler K. D., 2010, Handbook of Nanophysics: Nanotubes and Nanowires, CRC press.
[6] Biró L. P., Horváth Z. E., Márk G. I., Osváth Z., A.A. Koós , Benito A. M., Maser W., Lambin P., 2004, Carbon nanotube Y- junctions: growth and properties, Diamond and Related Materials 13: 241-249.
[7] Choi Y. C.,Choi W., 2005, Synthesis of Y-junction single-wall carbon nanotubes, Carbon 43: 2737-2741.
[8] Park J. H., Sinnott S. B., Aluru N. R., 2006, Ion separation using a Y-junction carbon nanotube, Nanotechnology 17: 895-900.
[9] Zhang J., Lu J., Xia Q., 2007, Research on the valveless piezoelectric pump with Y-shape pipes, Frontiers of Mechanical Engineering in China 2: 144-151.
[10] Filiz S., Aydogdu M., 2010, Axial vibration of carbon nanotube heterojunctions using nonlocal elasticity, Computational Materials Science 49: 619-627.
[11] Avramidis I. E., Morfidis K., 2006, Bending of beams on three-parameter elastic foundation, International Journal of Solids and Structures 43: 357-375.
[12] Challamel N., Meftah S. A., Bernard F., 2010, Buckling of elastic beams on nonlocal foundation: a revisiting of reissner model, Mechanics Research Communications 37: 472-475.
[13] Failla G., Santini A., Zingales M., 2012, A nonlocal two-dimensional foundation model, Archive of Applied Mechanics 83: 253-272.
[14] Shen H. S., 2011, A novel technique for nonlinear analysis of beams on two-parameter elastic foundations, International Journal of Structural Stability and Dynamics 11: 999-1014.
[15] 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: Low-Dimensional Systems and Nanostructures 45: 109-121.
[16] Besseghier A., Tounsi A., Houari M. S. A., Benzair A., Boumia L., Heireche H., 2011, Thermal effect on wave propagation in double-walled carbon nanotubes embedded in a polymer matrix using nonlocal elasticity, Physica E: Low-Dimensional Systems and Nanostructures 43: 1379-1386.
[17] Ghorbanpour Arani A., Roudbari M. A., 2014, Surface stress, initial stress and knudsen-dependent flow velocity effects on the electro-thermo nonlocal wave propagation of SWBNNTs, Physica B: Condensed Matter 452: 159-165.
[18] Ghorbanpour Arani A., Zarei M. S., Amir S., Khoddami Maraghi Z., 2013, Nonlinear nonlocal vibration of embedded DWCNT conveying fluid using shell model, Physica B: Condensed Matter 410: 188-196.
[19] Pak C. H., Hong S.C. S., Yun Y. S. Y., 1991, On the vibrations of three-dimensional angled piping systems conveying fluid, KSME Journal 5: 86-92.
[20] Eringen A. C., 2002, Nonlocal Continuum Field Theories, Springer.
[21] Kaviani F., Mirdamadi H.R., 2012, Influence of knudsen number on fluid viscosity for analysis of divergence in fluid conveying nano-tubes, Computational Materials Science 61: 270-277.
[22] 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: Engineering 45: 423-432.
[23] Gregory R.W., Paidoussis M. P., 1966, Unstable oscillation of tubular cantilevers conveying fluid.I.theoy, Proceedings of the Royal Society of London, Series A, Mathematical and Physical Sciences 293: 512-527.
[24] Zhen Y., Fang B., 2010, Thermal-mechanical and nonlocal elastic vibration of single-walled carbon nanotubes conveying fluid, Computational Materials Science 49: 276-282.