Smart Structures and Systems

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Analysis of nonlocal Kelvin's model for embedded microtubules: Via viscoelastic medium

  • Taj, Muhammad (Department of Mathematics, University of Azad Jammu and Kashmir) ;
  • Khadimallah, Mohamed A. (Prince Sattam Bin Abdulaziz University, College of Engineering, Civil Engineering Department) ;
  • Hussain, Muzamal (Department of Mathematics, Govt. College University Faisalabad) ;
  • Khedher, Khaled Mohamed (Department of Civil Engineering, College of Engineering, King Khalid University) ;
  • Shamim, Raja A. (Department of Mathematics, University of Azad Jammu and Kashmir) ;
  • Ahmad, Manzoor (Department of Mathematics, University of Azad Jammu and Kashmir) ;
  • Tounsi, Abdelouahed (YFL (Yonsei Frontier Lab), Yonsei University)
  • Received : 2020.06.09
  • Accepted : 2020.10.27
  • Published : 2020.12.25
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Abstract

In cells, the microtubules are surrounded by viscoelastic medium. Microtubules, though very small in size, perform a vital role in transportation of protein and in maintaining the cell shape. During performing these functions waves propagate and this propagation of waves has been investigated using nonlocal elastic theory. But the effect of surrounding medium was not taken into account. To fill this gap, this study considers the viscoelastic medium along with nonlocal elastic theory. The analytical formulas of the velocity of waves, and the results reveal that the presence of medium reduces the velocity. The axisymmetric and nonaxisymmetric waves are separately discussed. Furthermore, the results are compared with the results gained from the studies of free microtubules. The presence of medium around microtubules results in the increase of the flexural rigidity causing a significant decrease in radial wave velocity as compared to axial and circumferential wave velocities. The effect of viscoelastic medium is more obvious on radial wave velocity, to a lesser extent on torsional wave velocity and least on longitudinal wave velocity.

Keywords

Acknowledgement

The research team thanks the efforts of King Khalid University in financing this applied research and providing all the facilities (laboratories, hardware and software) in the College of Engineering. In addition, special thanks to Civil Engineering Department where this applied research work achieved. Finally, thanks again to Deanship of Scientific Research in King Khalid University to continue to support scientific research until it becomes among the best universities locally and internationally. Within the framework of small research projects given by the Deanship of Scientific Research the grant number is 305.

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