Bifurcation and chaos analysis of a pretensioned moving printed electronic laminated membrane considering aerothermoelasticity

Abstract

The bifurcation and chaotic motion characteristics are studied for a roll-to-roll flexible printed electronic laminated membrane subjected to initial tension in a steady temperature field. First, an aerodynamic model of the moving membrane is established by using an improved Newton's law for internal friction. Based on von Karman's large deflection theory, a nonlinear vibration differential equation is derived for the laminated membrane under multiple physical fields using Hamilton's principle and solved numerically using the fourth-order Runge-Kutta method. The effects of the temperature, air resistance and other parameters on the nonlinear vibration of the membrane are analyzed by using the bifurcation diagram, Lyapunov exponent diagram and corresponding phase diagram, Poincaré diagram and time history diagram. The results show that the membrane exhibits abundant chaos and bifurcation phenomena under a coupling field. The parameters of the membrane can be varied to control the nonlinear vibration characteristics. This study provides theoretical guidance for improving the transmission stability of electronic membranes and realizing high-precision overprinting.