Thermal stress effects on microtubules based on orthotropic model: Vibrational analysis

Muhammad Taj , Mohamed A. Khadimallah , Muzamal Hussain , Khurram Fareed , Muhammad Safeer , Khaled Mohamed Khedher , Manzoor Ahmad , M. Nawaz Naeem , Amjad Qazaq , Abdelaziz Al Qahtani , S.R. Mahmoud , Afaf S. Alwabli , Abdelouahed Tounsi

Abstract

Vibration of protein microtubules is investigated based upon Orthotropic Elastic Shell Model, considering the effect of thermal stresses. The complete analytical formulas of thermal vibration for microtubules are obtained. It is observed that the effects of thermal stresses on the vibrational frequency mode are more significant when the longitudinal and circumferential wave vectors are large enough. But when the length of wave vector reduces to 5 nm, these effects have no significant effects. The present results well agree with the lattice vibrations of microtubules. Moreover, the results show that the effects of thermal stresses due to small change in temperature are not so significant but with the increase in temperature its effects are obvious.

Key Words

microtubules; Hooks law; vibration; orthotropic; thermal stress

Address

Muhammad Taj — Department of Mathematics, University of Azad Jammu and Kashmir, Muzaffarabad, 1300, Azad Kashmir, Pakistan
Mohamed A. Khadimallah — Prince Sattam Bin Abdulaziz University, College of Engineering, Civil Engineering Department, Al-Kharj, 16273, Saudi Arabia; Laboratory of Systems and Applied Mechanics, Polytechnic School of Tunisia, University of Carthage, Tunis, Tunisia
Muzamal Hussain — Research Scholar, Department of Mathematics, Govt. College University Faisalabad, 38000, Faisalabad, Pakistan
Khurram Fareed — Department of Mathematics, University of Azad Jammu and Kashmir, Muzaffarabad, 1300, Azad Kashmir, Pakistan
Muhammad Safeer — Department of Mathematics, University of Azad Jammu and Kashmir, Muzaffarabad, 1300, Azad Kashmir, Pakistan
Khaled Mohamed Khedher — Department of Civil Engineering, College of Engineering, King Khalid University, Abha 61421, Saudi Arabia; Department of Civil Engineering, High Institute of Technological Studies, Mrezgua University Campus, Nabeul 8000, Tunisia
Manzoor Ahmad — Department of Mathematics, University of Azad Jammu and Kashmir, Muzaffarabad, 1300, Azad Kashmir, Pakistan
M. Nawaz Naeem — Research Scholar, Department of Mathematics, Govt. College University Faisalabad, 38000, Faisalabad, Pakistan
Amjad Qazaq — Prince Sattam Bin Abdulaziz University, College of Engineering, Civil Engineering Department, Al-Kharj, 16273, Saudi Arabia
Abdelaziz Al Qahtani — Prince Sattam Bin Abdulaziz University, College of Engineering, Civil Engineering Department, Al-Kharj, 16273, Saudi Arabia
S.R. Mahmoud — GRC Department, Faculty of Applied studies, King Abdulaziz University, Jeddah, Saudi Arabia
Afaf S. Alwabli — Department of Biological Sciences, Faculty of Science, King Abdulaziz University, Jeddah, Saudi Arabia
Abdelouahed Tounsi — YFL (Yonsei Frontier Lab), Yonsei University, Seoul, Korea; Department of Civil and Environmental Engineering, King Fahd University of Petroleum & Minerals, 31261 Dhahran, Eastern Province, Saudi Arabia

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