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Vibration response of Timoshenko perforated microbeams under accelerating load and thermal environment

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  • Abdelrahman, Alaa A.
  • Esen, Ismail
  • Eltaher, Mohamed A

Abstract

This article presents a dynamic finite elements procedure capable of analyzing the dynamic behavior of perforated Timoshenko microbeams in thermal environment and subjected to moving mass for the first time. An analytical geometrical model is presented to incorporate the perforation effect into the governing equations. The microstructure size dependent effect is incorporated based on the modified couple stress theory. Based on the presented geometrical model, the dynamic equations of motion including the interaction terms of the mass inertia are derived from the exact differential of the displacement functions of the beam relative to the mass contact point. To investigate the temperature effect on the dynamic behavior, thermal loading with different temperature rise profiles are considered. Thermal stresses, due to thermal loads are converted to mechanical stresses and then the thermal rigidity matrix is combined with the stiffness matrix of the beam. The dynamic finite element equations of motion are derived including the thermal effect. The system equations are solved numerically by using implicit time integration method due to its stability. The proposed numerical procedure is checked by comparing the obtained results with the available solutions and good agreement is observed. Effects of perforation parameters, thermal loading profile, moving mass characteristics, as well as the moving speed on the dynamic behavior of perforated microbeams are studied. The obtained results are helpful in the design and manufacturing of perforated microbeams structural systems.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:apmaco:v:407:y:2021:i:c:s0096300321003969
    DOI: 10.1016/j.amc.2021.126307
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    References listed on IDEAS

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    1. Eftekhari, S.A., 2021. "A simple finite element procedure for free vibration of rectangular thin and thick plates," Applied Mathematics and Computation, Elsevier, vol. 401(C).
    2. Ahn, Jeongho & Rail, Zachary, 2021. "A rod-beam system with dynamic contact and thermal exchange condition," Applied Mathematics and Computation, Elsevier, vol. 388(C).
    3. 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).
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    Cited by:

    1. 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).
    2. Nelson Andrés López Machado & Juan Carlos Vielma Pérez & Leonardo Jose López Machado & Vanessa Viviana Montesinos Machado, 2022. "An 8-Nodes 3D Hexahedral Finite Element and an 1D 2-Nodes Structural Element for Timoshenko Beams, Both Based on Hermitian Intepolation, in Linear Range," Mathematics, MDPI, vol. 10(5), pages 1-23, March.
    3. Babaei, Hadi, 2022. "Free vibration and snap-through instability of FG-CNTRC shallow arches supported on nonlinear elastic foundation," Applied Mathematics and Computation, Elsevier, vol. 413(C).

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