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A New Beam Element for Static, Free and Forced Vibration Responses of Microbeams Resting on Viscoelastic Foundation Based on Modified Couple Stress and Third-Order Beam Theories

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Iranian Journal of Science and Technology, Transactions of Mechanical Engineering Aims and scope Submit manuscript

Abstract

In this paper, a new beam element based on third-order Reddy beam theory and modified couple stress theory is introduced for static and dynamic analyses of microbeams. The beam is resting on Kelvin–Voigt-type viscoelastic foundation. Equilibrium equations are derived by using Hamilton’s principle. Galerkin finite element method is applied to the governing equations, and shape functions of the new beam element have been derived. As a result, applying only six elements are suitable for assessing beam behavior precisely, and it is beneficial due to the reduction in computation time. The proposed element is a two-node element with 4 degrees of freedom at each node. The effect of different stiffness and damping of viscoelastic foundation, boundary condition and length parameters on natural frequency and transient response of the microbeam is investigated.

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Authors and Affiliations

  1. Department of Mechanical Engineering, North Tehran Branch, Islamic Azad University, P.O.B. 1651153311, Tehran, Iran

    Reza Damghanian & Kamran Asemi

  2. Department of Mechanical Engineering, University of Eyvanekey, Eyvanekey, Semnan, Iran

    Masoud Babaei

Authors
  1. Reza Damghanian
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  2. Kamran Asemi
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  3. Masoud Babaei
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Correspondence to Kamran Asemi.

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Damghanian, R., Asemi, K. & Babaei, M. A New Beam Element for Static, Free and Forced Vibration Responses of Microbeams Resting on Viscoelastic Foundation Based on Modified Couple Stress and Third-Order Beam Theories. Iran J Sci Technol Trans Mech Eng 46, 131–147 (2022). https://doi.org/10.1007/s40997-020-00407-z

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  • DOI: https://doi.org/10.1007/s40997-020-00407-z

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