1.30

Impact Factor

2.10

CiteScore

# 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.

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

1. [1] S. Chakraverty, R. M. Jena, and S. K. Jena. Computational fractional dynamical systems: fractional differential equations and applications. John Wiley & Sons, 2022.
2. [2] R. Selvamani, M. M. S. Jayan, and F. Ebrahami, (2022) “Vibration analysis of magneto-elastic single-walled mass sensor carbon nanotube conveying pulsating viscous fluid based on Haar wavelet method" Partial Differential Equations in Applied Mathematics 6: 100428. DOI: 10.1177/0954406214538011.
3. [3] I. Al-Adwan, A. Awwad, M. Gaith, F. Alfaqs, Z. Haddadin, A. Wahbe, M. Hamam, M. Qunees, M. A. Khatib, and M. Bsaileh, (2023) “Modal analysis of simply supported tapered pipe transporting fluid with an edge crack using finite element method" International Journal of Mechanical Engineering and Robotics Research 12: 231–238. DOI: 10.18178/ijmerr.12.4.231-238.
4. [4] M. Hoseinzadeh, R. Pilafkan, and V. A. Maleki, (2023) “Size-dependent linear and nonlinear vibration of functionally graded CNT reinforced imperfect microplates submerged in fluid medium" Ocean Engineering 268: 113257. DOI: 10.1016/j.oceaneng.2022.113257.
5. [5] M. Nasrabadi, A. V. Sevbitov, V. A. Maleki, N. Akbar, and I. Javanshir, (2022) “Passive fluid-induced vibration control of viscoelastic cylinder using nonlinear energy sink" Marine Structures 81: 103116. DOI: 10.1016/j.marstruc.2021.103116.
6. [6] K. A. Lazopoulos, D. Karaoulanis, and A. K. Lazopoulos, (2022) “On Λ-fractiona visco-elastic beam" Forces in Mechanics 7: 100075. DOI: 10.1016/j.finmec.2022.100075.
7. [7] A. Fatahi-Vajari and Z. Azimzadeh, (2020) “Axial vibration of single-walled carbon nanotubes with fractional damping using doublet mechanics" Indian Journal of Physics 94: 975–986. DOI: 10.1007/s12648-019-01547-y.
8. [8] J. Lu and Y. Sun, (2023) “Analysis of the fractional oscillator for a mass attached to a stretched elastic wire" Journal of Low Frequency Noise, Vibration and Active Control: 1543–1559. DOI: 10.1177/14613484231181451.
9. [9] S. L. Guisquet and M. Amabili, (2021) “Identification by means of a genetic algorithm of nonlinear damping and stiffness of continuous structures subjected to largeamplitude vibrations. Part I: single-degree-of-freedom responses" Mechanical Systems and Signal Processing 153: 107470. DOI: 10.1016/j.ymssp.2020.107470.
10. [10] M. Amabili, P. Balasubramanian, and G. Ferrari. “Nonlinear Damping in Large-Amplitude Vibrations of Viscoelastic Plates”. In: 59469. American Society of Mechanical Engineers, 2019, V009T11A040. DOI: 10.1115/IMECE2019-10339.
11. [11] A. R. Askarian, M. R. Permoon, and M. Shakouri, (2020) “Vibration analysis of pipes conveying fluid resting on a fractional Kelvin-Voigt viscoelastic foundation with general boundary conditions" International Journal of Mechanical Sciences 179: 105702. DOI: 10.1016/j.ijmecsci.2020.105702.
12. [12] M. Javadi and M. Rahmanian, (2021) “Nonlinear vibration of fractional Kelvin–Voigt viscoelastic beam on nonlinear elastic foundation" Communications in Nonlinear Science and Numerical Simulation 98: 105784. DOI: 10.1016/j.cnsns.2021.105784.
13. [13] M. Javadi, M. A. Noorian, and S. Irani, (2019) “Primary and secondary resonances in pipes conveying fluid with the fractional viscoelastic model" Meccanica 54: 2081–2098. DOI: 10.1007/s11012-019-01068-2.
14. [14] R. Lewandowski and M. Baum, (2015) “Dynamic characteristics of multilayered beams with viscoelastic layers described by the fractional Zener model" Archive of Applied Mechanics 85: 1793–1814. DOI: 10.1007/s00419-015-1019-2.
15. [15] A. K. Jha and S. S. Dasgupta, (2019) “Mathematical modeling of a fractionally damped nonlinear nanobeam via nonlocal continuum approach" Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 233: 7101–7115.
16. [16] E. Loghman, A. Kamali, F. Bakhtiari-Nejad, and M. Abbaszadeh, (2021) “Nonlinear free and forced vibrations of fractional modeled viscoelastic FGM micro-beam" Applied Mathematical Modelling 92: 297–314. DOI: 10.1016/j.apm.2020.11.011.
17. [17] M. Qiu, D. Lei, and Z. Ou, (2022) “Nonlinear vibration analysis of fractional viscoelastic nanobeam" Journal of Vibration Engineering & Technologies: 1–24. DOI: 10.1007/s42417-022-00799-z.
18. [18] M. Bayat, I. Pakar, and A. Emadi, (2013) “Vibration of electrostatically actuated microbeam by means of homotopy perturbation method" Structural Engineering and Mechanics 48: 823–831.
19. [19] M. Bayat, M. Bayat, and M. Bayat, (2011) “An analytical approach on a mass grounded by linear and nonlinear springs in series" Int. J. Phys. Sci 6: 229–236. DOI: 10.5897/IJPS10.662.
20. [20] R. Ansari, M. F. Oskouie, and H. Rouhi, (2017) “Studying linear and nonlinear vibrations of fractional viscoelastic Timoshenko micro-/nano-beams using the strain gradient theory" Nonlinear Dynamics 87: 695–711. DOI: 10.1007/s11071-016-3069-6.
21. [21] R. Ansari, M. F. Oskouie, F. Sadeghi, and M. BazdidVahdati, (2015) “Free vibration of fractional viscoelastic Timoshenko nanobeams using the nonlocal elasticity theory" Physica E: Low-Dimensional Systems and Nanostructures 74: 318–327. DOI: 10.1016/j.physe. 2015.07.013.
22. [22] H. Farokhi and M. H. Ghayesh, (2016) “Size-dependent parametric dynamics of imperfect microbeams" International Journal of Engineering Science 99: 39–55. DOI: 10.1016/j.ijengsci.2015.10.014.

2.1
2023CiteScore

69th percentile