Forced vibration of fluid conveying carbon nanotubes considering thermal effect and nonlinear foundations

Abstract Nonlinear and linear vibrations of fluid conveying carbon nanotubes considering thermal effects are studied. It is assumed that the nanotube conveying fluid flow has a general type of boundary conditions and is supported on a nonlinear Winkler-Pasternak foundation. The nonlocal Euler-Bernoulli beam theory is implemented to develop the governing differential equation of motion of the nanotube system. Furthermore, the surface effect is considered in the vibration modelling of the carbon nanotubes. The influence of the thermal effect combined with the applied longitudinal force on the vibration performance of the system is examined. The Galerkin procedure is employed to obtain the nonlinear ordinary differential equation and the multiple time-scales method is utilized to study the primary vibration resonance of the system. A parametric sensitivity analysis is carried out to reveal the influence of different parameters on the vibration primary resonance and linear natural frequency. The effects of temperature variation, boundary conditions, foundation coefficients and the fluid flow velocity on the primary resonance and natural frequency of the nanotube are investigated. The effect of temperature on the material properties of carbon nanotube is originally combined with the vibration model. Different types of Zigzag carbon nanotubes are considered and the effects of different parameters, namely, the fluid flow velocity and the temperature variations are compared.

[1]  Sq Q. Shi,et al.  Strong mechanical coupling between the carbon nanotube and the inner streaming water flow , 2014 .

[2]  Xin Wang,et al.  The coupling vibration of fluid-filled carbon nanotubes , 2007 .

[3]  Baris Fidan,et al.  Parameter Identification and Adaptive Control Of Carbon Nanotube Resonators , 2018 .

[4]  Reza Ansari,et al.  BENDING BEHAVIOR AND BUCKLING OF NANOBEAMS INCLUDING SURFACE STRESS EFFECTS CORRESPONDING TO DIFFERENT BEAM THEORIES , 2011 .

[5]  Abdullah H. Sofiyev,et al.  Non-linear vibration of composite orthotropic cylindrical shells on the non-linear elastic foundations within the shear deformation theory , 2017 .

[6]  H. Askari.  Nonlinear vibration and chaotic motion of uniform and non-uniform carbon nanotube resonators. , 2014 .

[7]  Ebrahim Esmailzadeh,et al.  Multi-frequency excitation of stiffened triangular plates for large amplitude oscillations , 2014 .

[8]  Sung-kyun Kim,et al.  Flow-induced vibration and stability analysis of multi-wall carbon nanotubes , 2012 .

[9]  Toshiaki Natsuki,et al.  Prediction of elastic properties for single-walled carbon nanotubes , 2004 .

[10]  A. Sofiyev.  Large amplitude vibration of FGM orthotropic cylindrical shells interacting with the nonlinear Winkler elastic foundation , 2016 .

[11]  Lin Wang,et al.  The thermal effect on vibration and instability of carbon nanotubes conveying fluid , 2008 .

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

[13]  E. Shirani,et al.  A novel model for vibrations of nanotubes conveying nanoflow , 2012 .

[14]  Yong Su,et al.  STABILITY ANALYSIS OF A SINGLE-WALLED CARBON NANOTUBE CONVEYING PULSATING AND VISCOUS FLUID WITH NONLOCAL EFFECT , 2013 .

[15]  Win-Jin Chang,et al.  Free vibration of a single-walled carbon nanotube containing a fluid flow using the Timoshenko beam model , 2009 .

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

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

[18]  Toshiaki Natsuki,et al.  Wave propagation in single- and double-walled carbon nanotubes filled with fluids , 2007 .

[19]  Win-Jin Chang,et al.  Vibration analysis of a viscous-fluid-conveying single-walled carbon nanotube embedded in an elastic medium , 2009 .

[20]  K. Kishimoto,et al.  Scale effects on thermal buckling properties of carbon nanotube , 2010 .

[21]  N. Kuruoglu,et al.  Thermoelastic buckling of FGM conical shells under non-linear temperature rise in the framework of the shear deformation theory , 2017 .

[22]  Joan Adler,et al.  Vibrational analysis of thermal oscillations of single-walled carbon nanotubes under axial strain , 2014 .

[23]  Mohammad Hosseini,et al.  Vibration and instability analysis of nanotubes conveying fluid subjected to a longitudinal magnetic field , 2016 .

[24]  Ebrahim Esmailzadeh,et al.  Large Amplitude Free Vibration Analysis of Nanotubes Using Variational and Homotopy Methods , 2013 .

[25]  P. Soltani,et al.  Nonlinear flow-induced vibration of a SWCNT with a geometrical imperfection , 2012 .

[26]  H. R. Mirdamadi,et al.  Influence of Knudsen number on fluid viscosity for analysis of divergence in fluid conveying nano-tubes , 2012 .

[27]  Guido Herrmann,et al.  Real‐Time Sliding Mode Observer Scheme for Shear Force Estimation in a Transverse Dynamic Force Microscope , 2018 .

[28]  E. Esmailzadeh,et al.  Nonlinear vibration analysis of nonlocal nanowires , 2014 .

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

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

[31]  S. A. Fazelzadeh,et al.  Flow-thermoelastic vibration and instability analysis of viscoelastic carbon nanotubes embedded in viscous fluid , 2011 .

[32]  Mohammad Hassan Ghasemi,et al.  Analytical analysis of buckling and post-buckling of fluid conveying multi-walled carbon nanotubes , 2013 .

[33]  H. R. Mirdamadi,et al.  Effects of nonlocal elasticity and Knudsen number on fluid-structure interaction in carbon nanotube conveying fluid , 2012 .

[34]  A. Teimourian,et al.  Study on the effect of small scale on the wave reflection in carbon nanotubes using nonlocal Timoshenko beam theory and wave propagation approach , 2016 .

[35]  A comparative study on estimation of critical buckling temperatures of single-walled carbon nanotubes , 2016 .

[36]  T.-P. Chang,et al.  Stochastic FEM on nonlinear vibration of fluid-loaded double-walled carbon nanotubes subjected to a moving load based on nonlocal elasticity theory , 2013 .

[37]  X. Wang,et al.  Effect of Environmental Temperatures on Elastic Properties of Single-Walled Carbon Nanotube , 2007 .

[38]  B. Fang,et al.  Thermal–mechanical vibration and instability analysis of fluid-conveying double walled carbon nanotubes embedded in visco-elastic medium , 2011 .

[39]  C. Lim,et al.  Dynamics and stability of transverse vibrations of nonlocal nanobeams with a variable axial load , 2010 .

[40]  Xiaoqiao He,et al.  Dynamic behavior of triple-walled carbon nanotubes conveying fluid , 2009 .

[41]  Tai-Ping Chang.  Nonlinear thermal–mechanical vibration of flow-conveying double-walled carbon nanotubes subjected to random material property , 2013 .

[42]  Bao Wen-Xing,et al.  Simulation of Young's modulus of single-walled carbon nanotubes by molecular dynamics , 2004 .