Nonlinear superharmonic resonance and chaotic motion of a moving web under an intermediate nonlinear support

Jiajuan Qing; Jimei Wu; Shisheng Zhou; Mingyue Shao

Results in Physics (Oct 2023)

Nonlinear superharmonic resonance and chaotic motion of a moving web under an intermediate nonlinear support

Jiajuan Qing,
Jimei Wu,
Shisheng Zhou,
Mingyue Shao

Affiliations

Jiajuan Qing: School of Mechanical and Precision Instrument Engineering, Xi'an University of Technology, Xi’an 710048, China
Jimei Wu: 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.
Shisheng Zhou: 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; 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.
Mingyue Shao: School of Printing, Packaging Engineering and Digital Media Technology, Xi’an University of Technology, Xi’an 710054, China

Journal volume & issue: Vol. 53
p. 107009

Abstract

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Roll-to-roll manufacturing is the primary means of flexible electronics to facilitate scale-up production, and the web as the printed substrate is guided by the intermediate roller in this process. This paper aims to investigate the nonlinear superharmonic resonance and chaotic motion of a moving web under an intermediate nonlinear support. This support is modeled as a nonlinear elastic spring with linear and nonlinear stiffness, and the equation of motion of the web attached with nonlinear elastic support is derived from the D’Alembert principle and von Karman theory. The resulting equation is reduced to the two-degree ordinary differential equations via the Galerkin truncation, the superharmonic resonance responses of the web system are obtained by the multi-scale method, and the bifurcation analysis and stability are analyzed by the Runge-Kutta numerical method. The results indicate that the linear and nonlinear stiffnesses have a significant effect on amplitude-frequency responses and chaotic motion. This study provides an exploration of vibration behaviors of the web in flexible manufacturing, thereby laying the foundation for the improvement of fabrication productivity.

Published in Results in Physics

ISSN: 2211-3797 (Online)
Publisher: Elsevier
Country of publisher: Netherlands
LCC subjects: Science: Physics
Website: http://www.journals.elsevier.com/results-in-physics/

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