Nonlinear vibration characteristics of axially moving anisotropic membrane with gas-thermal-elastic coupling

Abstract

In the actual printing production process, the printing electronic motion membrane is susceptible to transverse vibration caused by interference from air drag, temperature changes, and other external conditions, resulting in membrane wrinkles, slippage, and other phenomena in the transmission process. We studied the bifurcation and chaos movement properties of anisotropic membranes under air drag and temperature. According to D’Alembert’s theory and von Kármán’s principle, the nonlinear dynamic differential formulas of axially moving anisotropic membranes with gas-thermal-elastic coupling are established. The Galerkin method is applied to discretize the formulas to obtain the state equation of the system. Finally, numerical simulations are performed by applying the fourth-order Runge–Kutta method to analyze the bifurcation and chaos of the system in terms of orthotropic coefficient, dimensionless air drags, and dimensionless temperature. The bifurcation diagrams, Lyapunov exponent diagrams, displacement time-history diagrams, phase-trajectory plane diagrams, and Poincaré diagrams of the membrane system are obtained. The results show that the anisotropic coefficient, dimensionless air drag, and dimensionless temperature significantly impact the investigated nonlinear dynamic of the anisotropic membrane, which provides a theoretical basis for production efficiency and high-quality printing equipment.