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Smart Structures and Systems Volume 26, Number 6, December 2020 , pages 809-817 DOI: https://doi.org/10.12989/sss.2020.26.6.809 |
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Analysis of nonlocal Kelvin's model for embedded microtubules: Via viscoelastic medium |
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Muhammad Taj, Mohamed A. Khadimallah, Muzamal Hussain, Khaled Mohamed Khedher, Raja A. Shamim, Manzoor Ahmad and Abdelouahed Tounsi
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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. | ||
| Key Words | ||
| microtubules; wave propagation; Kelvin model; viscoelastic medium | ||
| Address | ||
| (1) Muhammad Taj, Raja A. Shamim, Manzoor Ahmad: Department of Mathematics, University of Azad Jammu and Kashmir, Muzaffarabad, 1300, Azad Kashmir, Pakistan; (2) Mohamed A. Khadimallah: Prince Sattam Bin Abdulaziz University, College of Engineering, Civil Engineering Department, BP 655, Al-Kharj, 16273, Saudi Arabia; (3) Mohamed A. Khadimallah: Laboratory of Systems and Applied Mechanics, Polytechnic School of Tunisia, University of Carthage, Tunis, Tunisia; (4) Muzamal Hussain: Department of Mathematics, Govt. College University Faisalabad, 38000, Faisalabad, Pakistan; (5) Khaled Mohamed Khedher: Department of Civil Engineering, College of Engineering, King Khalid University, Abha 61421, Saudi Arabia; (6) Khaled Mohamed Khedher: Department of Civil Engineering, High Institute of Technological Studies, Mrezgua University Campus, Nabeul 8000, Tunisia; (7) Abdelouahed Tounsi: YFL (Yonsei Frontier Lab), Yonsei University, Seoul, Korea. | ||