Non-local orthotropic elastic shell model for vibration analysis of protein microtubules

Muhammad Taj, Afnan Majeed, Muzamal Hussain, Muhammad N. Naeem, Muhammad Safeer, Manzoor Ahmad, Hidayat Ullah Khan and Abdelouahed Tounsi

Abstract

Vibrational analysis in microtubules is examined based on the nonlocal theory of elasticity. The complete analytical formulas for wave velocity are obtained and the results reveal that the small scale effects can reduce the frequency, especially for large longitudinal wave-vector and large circumferential wave number. It is seen that the small scale effects are more significant for smaller wave length. The methods and results may also support the design and application of nano devices such as micro sound generator etc. The effects of small scale parameters can increase vibrational frequencies of the protein microtubules and cannot be overlooked in the analysis of vibrating phenomena. The results for different modes with nonlocal effect are checked.

Key Words

microtubules; nonlocal theory of elasticity; vibration analysis; small scale effects

Address

Muhammad Taj: Department of Mathematics, University of Azad Jammu and Kashmir, Muzaffarabad, 1300, Azad Kashmir, Pakistan Afnan Majeed: Department of Mathematics, University of Azad Jammu and Kashmir, Muzaffarabad, 1300, Azad Kashmir, Pakistan Muzamal Hussain: Department of Mathematics, Govt. College University Faisalabad, 38000, Faisalabad, Pakistan Muhammad N. Naeem: Department of Mathematics, Govt. College University Faisalabad, 38000, Faisalabad, Pakistan Muhammad Safeer: Department of Mathematics, University of Azad Jammu and Kashmir, Muzaffarabad, 1300, Azad Kashmir, Pakistan; Department of Mathematics, University of Poonch, Rawalwkot 12350, Azad Kashmir, Pakistan Manzoor Ahmad: Department of Mathematics, University of Azad Jammu and Kashmir, Muzaffarabad, 1300, Azad Kashmir, Pakistan Hidayat Ullah Khan: Department of Mathematics, University of Malakand at Chakdara, Dir (Lower), Khyber Pakhtoonkhwa, Pakistan Abdelouahed Tounsi: Materials and Hydrology Laboratory, University of Sidi Bel Abbes, Algeria Faculty of Technology Civil Engineering Department; Department of Civil and Environmental Engineering, King Fahd University of Petroleumand Minerals, 31261 Dhahran, Eastern Province, Saudi Arabia

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