Bifurcation and Chaos of Forced Vibration for a Viscoelastic Moving Membrane

• Published in: Journal of Vibration Engineering & Technologies Vol. 12; no. 3; pp. 4345 - 4355
• Main Authors: Wang, Jing, Zhou, Shisheng, Wu, Jimei, Shao, Mingyue, Dong, Guirong
• Format: Journal Article
• Language: English
• Published: Singapore Springer Nature Singapore 01.03.2024
• Subjects: Acoustics; Control; Dynamical Systems; Engineering; Engineering Acoustics; Original Paper; Vibration; Viscoelastic moving membrane; Bifurcation and chaos; Nonlinear; Forced vibration
• ISSN: 2523-3920; 2523-3939
• DOI: 10.1007/s42417-023-01123-z

Purpose The viscoelastic properties of PET membrane and the external force on the membrane during printing were considered, the bifurcation and chaos of nonlinear forced vibration of the viscoelastic moving membrane were studied in this paper. Methods Considering the geometric nonlinearity of the vibration of the membrane, the Kelvin constitutive equation was introduced, the external force on the moving membrane was modeled as a uniformly distributed simple harmonic force, and the nonlinear forced vibration equation of the viscoelastic moving membrane was established. The motion equation was discretized using Bubnov-Galerkin method, then the state equation of the viscoelastic printed membrane was obtained. The fourth-order Runge–Kutta method was used for numerical calculation. The displacement bifurcation, the largest Lyapunov exponent diagram, the time history diagram, the phase diagram and the Poincaré section under different parameters were obtained. Results and conclusions The findings indicate that the change of each parameter has a great influence on the bifurcation and chaos of the membrane. Appropriate parameters are the key to keeping good stability of the membrane.