Investigation of Nonlinear Thermo-Elastic Behavior of Fluid Conveying Piezoelectric Microtube Reinforced by Functionally Distributed Carbon Nanotubes on Viscoelastic-Hetenyi Foundation

Authors

  • Mehdi Azhdarzadeh Department of Mechanical Engineering, University of Alberta, Edmonton, AB, Canada
  • Reza Jahangiri Department of Mechanical Engineering, Azad University, Salmas Branch, Salmas, Iran
  • Akbar Allahverdizadeh Department of Mechatronics Engineering, University of Tabriz, Tabriz, Iran
  • Behnam Dadashzadeh Department of Mechatronics Engineering, University of Tabriz, Tabriz, Iran
  • Ramin Nabati Department of Mechanical Engineering, Azad University, Salmas Branch, Salmas, Iran

DOI:

https://doi.org/10.13052/ejcm2642-2085.3113

Keywords:

Microtube, Piezoelectric, Reinforced, Viscoelastic Foundation

Abstract

In this paper, nonlinear and nonlocal thermo-elastic behavior of a microtube reinforced by Functionally Distributed Carbon Nanotubes, with internal and external piezoelectric layers, in the presence of nonlinear viscoelastic-Hetenyi foundation, and axial fluid flow inside the microtube is studied. Nonlinear partial differential equations governing the system are derived using Reddy’s third-order shear deformations theory along with the Von-Karman theory including the effect of fluid viscosity. Then, the equations are converted to time-dependent ordinary nonlinear equations using the Galerkin method. Afterward, the governing equations of the microtube’s lateral displacements are solved using the multiple scales method. The analysis of the piezoelectric’s parametric resonance is performed by obtaining trivial and nontrivial stationary solutions and plotting characteristic curves of the frequency response and voltage response. At the end, the effect of different parameters including the flow velocity, excitation voltage, parameters of the foundation, viscosity parameter, thermal loading and nanotubes’ volume fraction index on the nonlinear behavior of the system, under parametric resonance condition, is investigated.

Downloads

Download data is not yet available.

Author Biographies

Mehdi Azhdarzadeh, Department of Mechanical Engineering, University of Alberta, Edmonton, AB, Canada

Mehdi Azhdarzadeh received his PhD in Mechanical Engineering from the University of Alberta, Canada. His research interests are aerosol and particle engineering, water treatment, robotics, controls, and mechanical modeling.

Reza Jahangiri, Department of Mechanical Engineering, Azad University, Salmas Branch, Salmas, Iran

Reza Jahangiri received his BSc, MSc, and PhD degree in mechanical engineering from the Urmia, Sharif University of Technology, and the University of Tabriz, respectively, Iran. After getting his PhD, he joined the faculty of engineering of Azad University, IRAN, where he is an assistant professor in the Mechanical Engineering Department. His current research interests are in the areas of fluid-induced nonlinear and chaotic magneto-piezo-aero-thermo_elastic behavior of the Beams/Plates/Shells using elasticity theories. Also, he is working in the field of nonlinear robust/fuzzy control and nano/microfluidic.

Akbar Allahverdizadeh, Department of Mechatronics Engineering, University of Tabriz, Tabriz, Iran

Akbar Allahverdizadeh teaches in the Department of Mechatronics Engineering at the University of Tabriz, Iran. He received his Bachelor’s degree in Mechanical Engineering from the Isfahan University of Technology, Iran in 2000 and his Master’s and Doctoral degrees in Mechanical Engineering from the University of Tehran, Iran in 2006 and 2013. His research interests are in the areas of mechatronics, biomechanics, and vibration control.

Behnam Dadashzadeh, Department of Mechatronics Engineering, University of Tabriz, Tabriz, Iran

Behnam Dadashzadeh is an assistant professor of mechatronics engineering at the University of Tabriz since 2013. He received his BSc from the University of Tabriz in 2005 and his MSc and PhD from the University of Tehran in 2007 and 2013, all in Mechanical Engineering. His research interests include dynamics and control of biped robots running and walking, mechatronic systems, mobile robots, and musculoskeletal biomechanics. He has international research experiences at the University of Calgary working on event-based control of bipedal running in 2012, at the Oregon State University working on modeling and control of ATRIAS in 2013, and at École Nationale d’ingénieurs de Tarbes working on actuation systems for robotic hands.

Ramin Nabati, Department of Mechanical Engineering, Azad University, Salmas Branch, Salmas, Iran

Ramin Nabati received his MSc in mechanical engineering from Azad University. His research interest is microfluidic.

References

S. H. Mirtalebi, M. T. Ahmadian, and A. Ebrahimi-Mamaghani, “On the dynamics of micro-tubes conveying fluid on various foundations,” SN Applied Sciences, vol. 1, no. 6, p. 547, May 2019, doi: 10.1007/s42452-019-0562-9.

Y. Zhen, Y. Gong, and Y. Tang, “Nonlinear vibration analysis of a supercritical fluid-conveying pipe made of functionally graded material with initial curvature,” Composite Structures, vol. 268, p. 113980, Jul. 2021, doi: 10.1016/j.compstruct.2021.113980.

Y. Zarabimanesh, P. Roodgar Saffari, P. Roudgar Saffari, and N. Refahati, “Hygro-thermo-mechanical vibration of two vertically aligned single-walled boron nitride nanotubes conveying fluid,” Journal of Vibration and Control, p. 10775463211006512, Mar. 2021, doi: 10.1177/10775463211006512.

F. Liang, A. Gao, X.-F. Li, and W.-D. Zhu, “Nonlinear parametric vibration of spinning pipes conveying fluid with varying spinning speed and flow velocity,” Applied Mathematical Modelling, vol. 95, pp. 320–338, Jul. 2021, doi: 10.1016/j.apm.2021.02.007.

P. Roodgar Saffari, M. Fakhraie, and M. A. Roudbari, “Size-Dependent Vibration Problem of Two Vertically-Aligned Single-Walled Boron Nitride Nanotubes Conveying Fluid in Thermal Environment Via Nonlocal Strain Gradient Shell Model,” Journal of Solid Mechanics, vol. 13, no. 2, pp. 164–185, 2021, doi: 10.22034/jsm.2020.1895313.1561.

P. R. Saffari, M. Fakhraie, and M. A. Roudbari, “Nonlinear vibration of fluid conveying cantilever nanotube resting on visco-pasternak foundation using non-local strain gradient theory,” Micro & Nano Letters, vol. 15, no. 3, pp. 181–186, Mar. 2020, doi: 10.1049/mnl.2019.0420.

B. Zhu, Q. Xu, M. Li, and Y. Li, “Nonlinear free and forced vibrations of porous functionally graded pipes conveying fluid and resting on nonlinear elastic foundation,” Composite Structures, vol. 252, p. 112672, Nov. 2020, doi: 10.1016/j.compstruct.2020.112672.

R. W. Gregory and M. P. Paidoussis, “Unstable oscillation of tubular cantilevers conveying fluid II. Experiments,” Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, vol. 293, no. 1435, pp. 528–542, 1966.

M. P. Paidoussis, Fluid-structure interactions: slender structures and axial flow, vol. 1. Academic press, 1998.

J. K. Sinha, S. Singh, and A. R. Rao, “Finite element simulation of dynamic behaviour of open-ended cantilever pipe conveying fluid,” Journal of sound and vibration, vol. 1, no. 240, pp. 189–194, 2001.

R. Ansari, R. Gholami, and A. Norouzzadeh, “Size-dependent thermo-mechanical vibration and instability of conveying fluid functionally graded nanoshells based on Mindlin’s strain gradient theory,” Thin-Walled Structures, vol. 105, pp. 172–184, 2016.

R. Ansari, R. Gholami, A. Norouzzadeh, and S. Sahmani, “Size-dependent vibration and instability of fluid-conveying functionally graded microshells based on the modified couple stress theory,” Microfluidics and nanofluidics, vol. 19, no. 3, pp. 509–522, 2015.

R. Ansari, A. Norouzzadeh, R. Gholami, M. F. Shojaei, and M. A. Darabi, “Geometrically nonlinear free vibration and instability of fluid-conveying nanoscale pipes including surface stress effects,” Microfluidics and nanofluidics, vol. 20, no. 1, p. 28, 2016.

M. Şimşek, “Nonlinear free vibration of a functionally graded nanobeam using nonlocal strain gradient theory and a novel Hamiltonian approach,” International Journal of Engineering Science, vol. 105, pp. 12–27, Aug. 2016, doi: 10.1016/j.ijengsci.2016.04.013.

A. Marzani, M. Mazzotti, E. Viola, P. Vittori, and I. Elishakoff, “FEM formulation for dynamic instability of fluid-conveying pipe on nonuniform elastic foundation,” Mechanics based design of structures and machines, vol. 40, no. 1, pp. 83–95, 2012.

X. Yang, T. Yang, and J. Jin, “Dynamic stability of a beam-model viscoelastic pipe for conveying pulsative fluid,” Acta Mechanica Solida Sinica, vol. 20, no. 4, pp. 350–356, 2007.

H. Liu, Z. Lv, and H. Tang, “Nonlinear vibration and instability of functionally graded nanopipes with initial imperfection conveying fluid,” Applied Mathematical Modelling, vol. 76, pp. 133–150, Dec. 2019, doi: 10.1016/j.apm.2019.06.011.

Z.-Q. Lu, K.-K. Zhang, H. Ding, and L.-Q. Chen, “Nonlinear vibration effects on the fatigue life of fluid-conveying pipes composed of axially functionally graded materials,” Nonlinear Dynamics, vol. 100, no. 2, pp. 1091–1104, Apr. 2020, doi: 10.1007/s11071-020-05577-8.

K. Zhou, Q. Ni, L. Wang, and H. L. Dai, “Planar and non-planar vibrations of a fluid-conveying cantilevered pipe subjected to axial base excitation,” Nonlinear Dynamics, vol. 99, no. 4, pp. 2527–2549, Mar. 2020, doi: 10.1007/s11071-020-05474-0.

H. Ding, J. Ji, and L.-Q. Chen, “Nonlinear vibration isolation for fluid-conveying pipes using quasi-zero stiffness characteristics,” Mechanical Systems and Signal Processing, vol. 121, pp. 675–688, Apr. 2019, doi: 10.1016/j.ymssp.2018.11.057.

L. Wang and Q. Ni, “On vibration and instability of carbon nanotubes conveying fluid,” Computational Materials Science, vol. 43, no. 2, pp. 399–402, 2008.

T. P. Chang, “Thermal-mechanical vibration and instability of a fluid-conveying single-walled carbon nanotube embedded in an elastic medium based on nonlocal elasticity theory,” Applied Mathematical Modelling, vol. 36, no. 5, pp. 1964–1973, 2012.

M. Rafiee, J. Yang, and S. Kitipornchai, “Thermal bifurcation buckling of piezoelectric carbon nanotube reinforced composite beams,” Computers & Mathematics with Applications, vol. 66, no. 7, pp. 1147–1160, 2013.

M. Rasekh and S. E. Khadem, “Nonlinear vibration and stability analysis of axially loaded embedded carbon nanotubes conveying fluid,” Journal of Physics D: Applied Physics, vol. 42, no. 13, p. 135112, 2009.

J. H. Yang, J. Yang, and S. Kitipornchai, “Nonlinear dynamic response of electro-thermo-mechanically loaded piezoelectric cylindrical shell reinforced with BNNTs,” Smart Materials and Structures, vol. 21, no. 12, p. 125005, 2012.

A. Alibeigloo, “Free vibration analysis of functionally graded carbon nanotube-reinforced composite cylindrical panel embedded in piezoelectric layers by using theory of elasticity,” European Journal of Mechanics-A/Solids, vol. 44, pp. 104–115, 2014.

M. Mohammadimehr and M. Mahmudian-Najafabadi, “Bending and free vibration analysis of nonlocal functionally graded nanocomposite Timoshenko beam model rreinforced by SWBNNT based on modified coupled stress theory,” Journal of Nanostructures, vol. 3, no. 4, pp. 483–492, 2013.

M. Mohammadimehr, M. Salemi, and B. R. Navi, “Bending, buckling, and free vibration analysis of MSGT microcomposite Reddy plate reinforced by FG-SWCNTs with temperature-dependent material properties under hydro-thermo-mechanical loadings using DQM,” Composite Structures, vol. 138, pp. 361–380, 2016.

H. Zhang et al., “Analysis of functionally graded carbon nanotube-reinforced composite structures: A review,” Nanotechnology Reviews, vol. 9, pp. 1408–1426, Dec. 2020, doi: 10.1515/ntrev-2020-0110.

A. H. Nayfeh and D. T. Mook, Nonlinear oscillations. John Wiley & Sons, 2008.

A. Ghorbanpour Arani, E. Haghparast, and Z. Khoddami Maraghi, “Vibration analysis of double bonded composite pipe reinforced by BNNTs conveying oil,” Journal of Computational Applied Mechanics, vol. 46, no. 2, pp. 93–105, 2015, doi: 10.22059/jcamech.2015.55092.

P. Zhu and K. M. Liew, “Free vibration analysis of moderately thick functionally graded plates by local Kriging meshless method,” Composite Structures, vol. 93, no. 11, pp. 2925–2944, 2011.

A. C. Eringen, “On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves,” Journal of applied physics, vol. 54, no. 9, pp. 4703–4710, 1983.

W. Zhang, J. Yang, and Y. Hao, “Chaotic vibrations of an orthotropic FGM rectangular plate based on third-order shear deformation theory,” Nonlinear Dynamics, vol. 59, no. 4, pp. 619–660, 2010.

M. Amabili and S. Farhadi, “Shear deformable versus classical theories for nonlinear vibrations of rectangular isotropic and laminated composite plates,” Journal of sound and vibration, vol. 320, no. 3, pp. 649–667, 2009.

Y. Fu and J. Ruan, “Nonlinear active control of damaged piezoelectric smart laminated plates and damage detection,” Applied Mathematics and Mechanics, vol. 29, no. 4, pp. 421–436, 2008.

L. Wang, “A modified nonlocal beam model for vibration and stability of nanotubes conveying fluid,” Physica E: Low-dimensional Systems and Nanostructures, vol. 44, no. 1, pp. 25–28, 2011.

X. Y. Guo, W. Zhang, and M. Yao, “Nonlinear dynamics of angle-ply composite laminated thin plate with third-order shear deformation,” Science China Technological Sciences, vol. 53, no. 3, pp. 612–622, 2010.

M. Mirzaei and Y. Kiani, “Thermal Buckling of Temperature Dependent FG-CNT Reinforced Composite Plates,” Meccanica, vol. 51, pp. 2185–2201, Sep. 2016, doi: 10.1007/s11012-015-0348-0.

Published

2022-05-07

Issue

Section

Original Article