Forced vibrations of viscoelastic microbeam using fractional order viscoelastic model

Zhenkun  Wang; Zhaoyu  Teng

doi:10.6180/jase.202410_27(10).0010

Forced vibrations of viscoelastic microbeam using fractional order viscoelastic model

$Forced vibrations of viscoelastic microbeam using fractional order viscoelastic model$

Zhenkun Wang and Zhaoyu TengThis email address is being protected from spambots. You need JavaScript enabled to view it.

The Second XiangYa Hospital of CentralSouth University, Changsha 410000, Hunan, China

Received: May 2, 2023
Accepted: September 3, 2023
Publication Date: January 4, 2024

Copyright The Author(s). This is an open access article distributed under the terms of the Creative Commons Attribution License (CC BY 4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are cited.

Download Citation: ||https://doi.org/10.6180/jase.202410_27(10).0010

This study investigates the dynamic behavior of a microbeam modeled using the Kelvin-Voigt fractional viscoelastic model. The microbeam is modeled using modified couple stress theory (MCST) and the fractional Kelvin-Voigt viscoelastic model. Following Hamilton’s principle, the governing equations of motion were expressed as a fractional order equation with partial derivatives. Combining finite elements and finite difference methods solves the obtained equation. The finite difference is used to discretize the equations in the time domain, and finite elements and Galerkin are used to discretize the equations in the space domain. As a result of the simulations, it has been demonstrated that the derivative of the fractional order greatly influences the range and time response of the free and forced vibrations of the microbeam, as well as the effects of dampening on the microbeam. Furthermore, the effects of small size parameters and viscoelastic damping coefficient have been investigated. Based on the results, the fractional order derivative substantially influences the resonance regions.

Keywords: Microbeam; Forced vibrations; Viscoelastic; Fractional order derivative

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