Vibration and instability analysis of nanotubes conveying fluid subjected to a longitudinal magnetic field

Abstract Based on the nonlocal elasticity theory, a nonlocal beam model is utilized to investigate the effect of a longitudinal magnetic field on the transverse vibration of a magnetically sensitive single-walled carbon nanotube (SWCNT) conveying fluid. The effect of longitudinal magnetic field is considered through the Lorentz magnetic force obtained from Maxwell's relations. Hamilton's principle is applied to the energy expressions to derive the higher-order FSI governing equation and the corresponding higher-order boundary conditions. In the solution part the differential transformation method (DTM) is used to solve the higher-order differential equations of motion. The effects of longitudinal magnetic field and nonlocal parameter on the vibration frequency and divergence instability of SWCNT conveying fluid are investigated. It can be concluded that the longitudinal magnetic field increases the critical flow velocities and the natural frequencies of the SWCNT. Numerical results from the model show that the fundamental natural frequency and critical flow velocity for the SWCNT increase as the nonlocal parameter increases, while in the presence of a strong longitudinal magnetic field the influence of internal fluid flow and nonlocal parameter on the vibrational frequencies of SWCNT can be reduced.

[1]  Reza Ansari,et al.  Vibrations of single- and double-walled carbon nanotubes with layerwise boundary conditions: A molecular dynamics study , 2012 .

[2]  L. Wang,et al.  Application of the differential transformation method to vibration analysis of pipes conveying fluid , 2011, Appl. Math. Comput..

[3]  Ni Qiao,et al.  In-plane vibration analyses of curved pipes conveying fluid using the generalized differential quadrature rule , 2008 .

[4]  Yan Yan,et al.  Dynamical behaviors of fluid-conveyed multi-walled carbon nanotubes , 2009 .

[5]  S. K. Park,et al.  Bernoulli–Euler beam model based on a modified couple stress theory , 2006 .

[6]  Lixiang Zhang,et al.  DYNAMICAL BEHAVIORS OF FLUID-FILLED MULTI-WALLED CARBON NANOTUBES , 2010 .

[7]  Win-Jin Chang,et al.  Computation of chirality- and size-dependent surface Young's moduli for single-walled carbon nanotubes , 2007 .

[8]  X. Wang,et al.  Transient response of carbon nanotubes with inhomogeneous coating under radial impact loading and magnetic field , 2013 .

[9]  T.-P. Chang,et al.  Thermal–mechanical vibration and instability of a fluid-conveying single-walled carbon nanotube embedded in an elastic medium based on nonlocal elasticity theory , 2012 .

[10]  M. A. McCarthy,et al.  Vibration response of double-walled carbon nanotubes subjected to an externally applied longitudinal magnetic field: A nonlocal elasticity approach , 2012 .

[11]  Hashem Rafii-Tabar,et al.  Computational modelling of the flow of viscous fluids in carbon nanotubes , 2007 .

[12]  Jingshuang Shen,et al.  Rigorous van der Waals effect on vibration characteristics of multi-walled carbon nanotubes under a transverse magnetic field , 2012 .

[13]  Chunyu Li,et al.  Vibrational behaviors of multiwalled-carbon-nanotube-based nanomechanical resonators , 2004 .

[14]  Win-Jin Chang,et al.  Free transverse vibration of the fluid-conveying single-walled carbon nanotube using nonlocal elastic theory , 2008 .

[15]  A. Eringen.  On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves , 1983 .

[16]  Sondipon Adhikari,et al.  NONLOCAL VIBRATION OF CARBON NANOTUBES WITH ATTACHED BUCKYBALLS AT TIP , 2011 .

[17]  Seyed Abdolrahim Atashipour,et al.  Vibration analysis of single-walled carbon nanotubes conveying nanoflow embedded in a viscoelastic medium using modified nonlocal beam model , 2014 .

[18]  NONLOCAL VIBRATION OF EMBEDDED COUPLED CNTS CONVEYING FLUID UNDER THERMO-MAGNETIC FIELDS VIA RITZ METHOD , 2013 .

[19]  Lin Wang.  A MODIFIED NONLOCAL BEAM MODEL FOR VIBRATION AND STABILITY OF NANOTUBES CONVEYING FLUID , 2011 .

[20]  W. Thomson.  Theory of vibration with applications , 1965 .

[21]  P. Soltani,et al.  PERIODIC SOLUTION FOR NONLINEAR VIBRATION OF A FLUID-CONVEYING CARBON NANOTUBE, BASED ON THE NONLOCAL CONTINUUM THEORY BY ENERGY BALANCE METHOD , 2012 .

[22]  C. Lim.  On the truth of nanoscale for nanobeams based on nonlocal elastic stress field theory: equilibrium, governing equation and static deflection , 2010 .

[23]  Litao Yin,et al.  Strain gradient beam model for dynamics of microscale pipes conveying fluid , 2011 .

[24]  Omer San,et al.  DYNAMICS OF PULSATILE FLOWS THROUGH ELASTIC MICROTUBES , 2010, 1212.0187.

[25]  S. K. Park,et al.  Variational formulation of a modified couple stress theory and its application to a simple shear problem , 2008 .

[26]  I. Mönch,et al.  Towards molecular spintronics: magnetotransport and magnetism in carbon nanotube-based systems , 2003 .

[27]  Fan Yang,et al.  Experiments and theory in strain gradient elasticity , 2003 .

[28]  A. G. Arani,et al.  Size‐dependent vibration of double‐bonded carbon nanotube‐reinforced composite microtubes conveying fluid under longitudinal magnetic field , 2016 .

[29]  X. Wang,et al.  Dynamic characteristics of multi-walled carbon nanotubes under a transverse magnetic field , 2011 .

[30]  T. Ebbesen.  Carbon Nanotubes: Preparation and Properties , 1996 .

[31]  A. Tounsi,et al.  Comment on “Free transverse vibration of the fluid-conveying single-walled carbon nanotube using nonlocal elastic theory” [J. Appl. Phys. 103, 024302 (2008)] , 2009 .

[32]  Wenhui Duan,et al.  CALIBRATION OF NONLOCAL SCALING EFFECT PARAMETER FOR FREE VIBRATION OF CARBON NANOTUBES BY MOLECULAR DYNAMICS , 2007 .

[33]  Lin Wang,et al.  Buckling instability of double-wall carbon nanotubes conveying fluid , 2008 .

[34]  T. Murmu,et al.  Nonlocal frequency analysis of nanoscale biosensors , 2012 .

[35]  S. Iijima.  Helical microtubules of graphitic carbon , 1991, Nature.

[36]  A. Mioduchowski,et al.  Vibration and instability of carbon nanotubes conveying fluid , 2005 .

[37]  Cha'o-Kuang Chen,et al.  Application of differential transformation to eigenvalue problems , 1996 .

[38]  Alessandro Marzani,et al.  Critical Flow Speeds of Pipes Conveying Fluid Using the Generalized Differential Quadrature Method , 2010 .

[39]  K. M. Liew,et al.  Nonlocal continuum model and molecular dynamics for free vibration of single-walled carbon nanotubes. , 2011, Journal of nanoscience and nanotechnology.

[40]  Abbas Assadi,et al.  Size dependent forced vibration of nanoplates with consideration of surface effects , 2013 .

[41]  A. G. Arani,et al.  Nonlocal vibration and instability analysis of embedded DWCNT conveying fluid under magnetic field with slip conditions consideration , 2015 .

[42]  M. Hosseini,et al.  The effects of non-uniform flow velocity on vibrations of single-walled carbon nanotube conveying fluid , 2015 .

[43]  Lin Wang,et al.  Size-dependent vibration characteristics of fluid-conveying microtubes , 2010 .

[44]  Bo Fang,et al.  Nonlinear vibration analysis of double-walled carbon nanotubes based on nonlocal elasticity theory , 2013 .

[45]  A. Sharma,et al.  Dramatic Improvement in properties of magnetically aligned CNT/polymer nanocomposites , 2010 .

[46]  S. Narendar,et al.  Wave propagation in single-walled carbon nanotube under longitudinal magnetic field using nonlocal Euler–Bernoulli beam theory , 2012 .

[47]  A. Eringen,et al.  Nonlocal Continuum Field Theories , 2002 .