Chaotic dynamics of fractional viscoelastic PET membranes subjected to combined harmonic and variable axial loads
Nonlinear chaotic vibrations of fractional viscoelastic PET (polyethylene terephthalate) membranes subjected to combined harmonic and variable axial loads is investigated in this paper. Axial tension variations arise from the machine disturbances of the processing line of roll-to-roll manufacturing....
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| Language: | English |
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Elsevier
2024-01-01
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| Series: | Results in Physics |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S2211379723009956 |
| _version_ | 1797350944829079552 |
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| author | Jiajuan Qing Shisheng Zhou Jimei Wu Mingyue Shao |
| author_facet | Jiajuan Qing Shisheng Zhou Jimei Wu Mingyue Shao |
| author_sort | Jiajuan Qing |
| collection | DOAJ |
| description | Nonlinear chaotic vibrations of fractional viscoelastic PET (polyethylene terephthalate) membranes subjected to combined harmonic and variable axial loads is investigated in this paper. Axial tension variations arise from the machine disturbances of the processing line of roll-to-roll manufacturing. The viscoelasticity of PET membrane is characterized by the fractional Kelvin-Voigt model. Based on the Hamilton principle, the equation of motion of the membrane is established with the consideration of geometric nonlinearity, and the Galerkin procedure is employed to discretize the resulting governing equation. For the solution, the finite difference method is utilized in conjunction with the Caputo-type fractional derivative to reliably estimate the nonlinear response of fractional viscoelastic PET membrane. The reliability of this numerical strategy is proved by the available results of the fractional system and comparison examples. The influence of system parameters on chaotic behaviors is described by the bifurcation diagram and the detailed responses at the set bifurcation parameters. The fractional model together with the analysis provides a fundamental framework for the control of viscoelastic substrates in flexible manufacturing. |
| first_indexed | 2024-03-08T12:52:24Z |
| format | Article |
| id | doaj.art-7409067eb03049348d335f6795029cf1 |
| institution | Directory Open Access Journal |
| issn | 2211-3797 |
| language | English |
| last_indexed | 2024-03-08T12:52:24Z |
| publishDate | 2024-01-01 |
| publisher | Elsevier |
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| series | Results in Physics |
| spelling | doaj.art-7409067eb03049348d335f6795029cf12024-01-20T04:44:54ZengElsevierResults in Physics2211-37972024-01-0156107202Chaotic dynamics of fractional viscoelastic PET membranes subjected to combined harmonic and variable axial loadsJiajuan Qing0Shisheng Zhou1Jimei Wu2Mingyue Shao3School of Mechanical and Precision Instrument Engineering, Xi'an University of Technology, Xi’an 710048, ChinaSchool of Mechanical and Precision Instrument Engineering, Xi'an University of Technology, Xi’an 710048, China; School of Printing, Packaging Engineering and Digital Media Technology, Xi’an University of Technology, Xi’an 710054, China; Shaanxi Provincial Key Laboratory of Printing and Packaging Engineering, Xi’an University of Technology, Xi’an 710048, China; Corresponding authors at: School of Mechanical and Precision Instrument Engineering, Xi'an University of Technology, Xi’an 710048, China.School of Mechanical and Precision Instrument Engineering, Xi'an University of Technology, Xi’an 710048, China; School of Printing, Packaging Engineering and Digital Media Technology, Xi’an University of Technology, Xi’an 710054, China; Corresponding authors at: School of Mechanical and Precision Instrument Engineering, Xi'an University of Technology, Xi’an 710048, China.School of Printing, Packaging Engineering and Digital Media Technology, Xi’an University of Technology, Xi’an 710054, ChinaNonlinear chaotic vibrations of fractional viscoelastic PET (polyethylene terephthalate) membranes subjected to combined harmonic and variable axial loads is investigated in this paper. Axial tension variations arise from the machine disturbances of the processing line of roll-to-roll manufacturing. The viscoelasticity of PET membrane is characterized by the fractional Kelvin-Voigt model. Based on the Hamilton principle, the equation of motion of the membrane is established with the consideration of geometric nonlinearity, and the Galerkin procedure is employed to discretize the resulting governing equation. For the solution, the finite difference method is utilized in conjunction with the Caputo-type fractional derivative to reliably estimate the nonlinear response of fractional viscoelastic PET membrane. The reliability of this numerical strategy is proved by the available results of the fractional system and comparison examples. The influence of system parameters on chaotic behaviors is described by the bifurcation diagram and the detailed responses at the set bifurcation parameters. The fractional model together with the analysis provides a fundamental framework for the control of viscoelastic substrates in flexible manufacturing.http://www.sciencedirect.com/science/article/pii/S2211379723009956Viscoelastic PET membraneCombined loadsChaotic vibrationsCaputo-type fractional derivative |
| spellingShingle | Jiajuan Qing Shisheng Zhou Jimei Wu Mingyue Shao Chaotic dynamics of fractional viscoelastic PET membranes subjected to combined harmonic and variable axial loads Results in Physics Viscoelastic PET membrane Combined loads Chaotic vibrations Caputo-type fractional derivative |
| title | Chaotic dynamics of fractional viscoelastic PET membranes subjected to combined harmonic and variable axial loads |
| title_full | Chaotic dynamics of fractional viscoelastic PET membranes subjected to combined harmonic and variable axial loads |
| title_fullStr | Chaotic dynamics of fractional viscoelastic PET membranes subjected to combined harmonic and variable axial loads |
| title_full_unstemmed | Chaotic dynamics of fractional viscoelastic PET membranes subjected to combined harmonic and variable axial loads |
| title_short | Chaotic dynamics of fractional viscoelastic PET membranes subjected to combined harmonic and variable axial loads |
| title_sort | chaotic dynamics of fractional viscoelastic pet membranes subjected to combined harmonic and variable axial loads |
| topic | Viscoelastic PET membrane Combined loads Chaotic vibrations Caputo-type fractional derivative |
| url | http://www.sciencedirect.com/science/article/pii/S2211379723009956 |
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