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Copyright © 2022 Zhe Zhang et al. This is an open access article distributed under the Creative Commons Attribution License (the “License”), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License. https://creativecommons.org/licenses/by/4.0/

Abstract

The nonlinear vibrations of an axially moving viscoelastic beam under the transverse harmonic excitation are examined. The governing equation of motion of the viscoelastic beam is discretized into a Duffing system with nonlinear fractional derivative using Galerkin’s method. The viscoelasticity of the moving beam is described by the fractional Kelvin–Voigt model based on the Caputo definition. The primary resonance is analytically investigated by the averaging method. With the aid of response curves, a parametric study is conducted to display the influences of the fractional order and the viscosity coefficient on steady-state responses. The validations of this study are given through comparisons between the analytical solutions and numerical ones, where the stability of the solutions is determined by the Routh–Hurwitz criterion. It is found that suppression of undesirable responses can be achieved via changing the viscosity of the system.

Details

Title
Nonlinear Vibrations of an Axially Moving Beam with Fractional Viscoelastic Damping
Author
Zhang, Zhe 1 ; Yang, Hongxiang 2   VIAFID ORCID Logo  ; Guo, Zhongjin 3 ; Zhu, Lili 2 ; Liu, Weiyan 3 

 College of Civil Engineering, Hunan University of Technology, Zhuzhou, Hunan 412007, China 
 School of Information Science and Technology, Taishan University, Taian, Shandong, China 
 School of Mathematics and Statics, Taishan University, Taian, Shandong, China 
Editor
Ping Xiang
Publication year
2022
Publication date
2022
Publisher
John Wiley & Sons, Inc.
ISSN
16878086
e-ISSN
16878094
Source type
Scholarly Journal
Language of publication
English
ProQuest document ID
2701960101
Copyright
Copyright © 2022 Zhe Zhang et al. This is an open access article distributed under the Creative Commons Attribution License (the “License”), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License. https://creativecommons.org/licenses/by/4.0/