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Application of exact continuum size-dependent theory for stability and frequency analysis of a curved cantilevered microtubule by considering viscoelastic properties

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Abstract

The stability analysis of cantilevered curved microtubules in axons regarding various size elements and using the generalized differential quadrature method for solving equations is reported. The impacts of covering MAP Tau proteins along with cytoplasm are taken into account as the elastic medium. Curved cylindrical nanoshell considering thick wall is used to model the microtubules. The factor of length scale (l/R = 0.2) used in modified couple stress theory would result in more accuracy when it comes to comparison with experiments, while alternative theories presented in this paper provide less precise outcomes. Due to the reported precise results, at the lower value of the time-dependent viscoelastic factor (\({\tau }_{s})\) by rising the size-dependent factor, the frequency response of the cantilever microtubule increases and this relation between the size-dependent parameter and the structure’s natural frequency is changed from direct to indirect for the higher amount of the time-based viscoelastic factor that scientists should attend to this matter when it comes to the microtubule. Furthermore, physical neighboring situations in a cell will be prominent in microtubules’ dynamic stability responses, such as membrane and cell-matrix. Since microtubules are likely to be applied as biosensors, this feature could be employed to disclose virulent tumors.

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Authors and Affiliations

  1. Division of Computational Mathematics and Engineering, Institute for Computational Science, Ton Duc Thang University, Ho Chi Minh City, 758307, Vietnam

    Ali Shariati

  2. Faculty of Civil Engineering, Ton Duc Thang University, Ho Chi Minh City, 758307, Vietnam

    Ali Shariati

  3. Center of Excellence in Design, Robotics, and Automation, School of Mechanical Engineering, Sharif University of Technology, Tehran, Iran

    Mostafa Habibi

  4. Material and Hydrology Laboratory, Civil Engineering Department, Faculty of Technology, University of Sidi Bel Abbes, Sidi Bel Abbès, Algeria

    Abdelouahed Tounsi

  5. Department of Mechanics, Imam Khomeini International University, Qazvin, Iran

    Hamed Safarpour

  6. Institute of Research and Development, Duy Tan University, Da Nang, 550000, Vietnam

    Maryam Safa

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  1. Ali Shariati
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  2. Mostafa Habibi
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  3. Abdelouahed Tounsi
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Shariati, A., Habibi, M., Tounsi, A. et al. Application of exact continuum size-dependent theory for stability and frequency analysis of a curved cantilevered microtubule by considering viscoelastic properties. Engineering with Computers 37, 3629–3648 (2021). https://doi.org/10.1007/s00366-020-01024-9

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