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Dynamic analysis of bi-directional functionally graded Timoshenko nanobeam on the basis of Eringen's nonlocal theory incorporating the surface effect

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  • Lal, Roshan
  • Dangi, Chinika

Abstract

In this article, a nonlocal model based on the Timoshenko beam theory has been introduced for vibration response of bi-directional functionally graded moderately thick nanobeam under the influence of surface effect. Surface and nonlocal effects have been accounted using the Gurtin-Murdoch surface elasticity theory and Eringen's nonlocal theory, respectively. The material properties of the beam are changing according to the power-law distribution in both the thickness and length directions. Employing Hamilton's energy principle, the governing equations of motion and corresponding boundary conditions have been extracted. The numerical results for frequency parameter have been obtained using the differential quadrature method for three different combinations of clamped and simply supported edge conditions. The study reveals that the consideration of surface and nonlocal effects in predicting the vibration characteristics of bi-directional functionally graded shear deformable nanobeam plays an important role and can't be ignored in the analysis. The results are validated by comparing with those available in the literature.

Suggested Citation

  • Lal, Roshan & Dangi, Chinika, 2021. "Dynamic analysis of bi-directional functionally graded Timoshenko nanobeam on the basis of Eringen's nonlocal theory incorporating the surface effect," Applied Mathematics and Computation, Elsevier, vol. 395(C).
    • Handle: RePEc:eee:apmaco:v:395:y:2021:i:c:s0096300320308109
    DOI: 10.1016/j.amc.2020.125857
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    Cited by:

    1. Abdelrahman, Alaa A. & Esen, Ismail & Eltaher, Mohamed A, 2021. "Vibration response of Timoshenko perforated microbeams under accelerating load and thermal environment," Applied Mathematics and Computation, Elsevier, vol. 407(C).
    2. Jahangiri, M. & Asghari, M., 2023. "The strain gradient-based torsional vibration analysis of micro-rotors with nonlinear flexural-torsional coupling," Applied Mathematics and Computation, Elsevier, vol. 440(C).
    3. Ma, Xiao & Zhou, Bo & Xue, Shifeng, 2022. "A Hermite interpolation element-free Galerkin method for functionally graded structures," Applied Mathematics and Computation, Elsevier, vol. 419(C).
    4. Wang, Xiaofeng & Xue, Wenlong & He, Yong & Zheng, Fu, 2023. "Uniformly exponentially stable approximations for Timoshenko beams," Applied Mathematics and Computation, Elsevier, vol. 451(C).

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