Nonlinear vibration of a moving flexible printed electron web under multiphysics dynamics

Flexible electronic printing technology is a scientific technology that uses an “ink” material with conductive, dielectric, or semiconductor properties printed on a flexible web substrate to achieve precise preparation of flexible electronic devices, which are widely used in information, energy, medical, and military fields. In the preparation of the printing process of flexible printed electron webs under complex working conditions, the moving web will experience substantial unstable nonlinear dynamic behavior, such as divergence, flutter, bifurcation, and chaos. Accordingly, because of the coupling effects of the complex working conditions of the magnetic field, air and nonlinear electrostatic field forces, it is indispensable to explore the nonlinear dynamic equation of the flexible printed electron web in motion. The theory of multiphysics dynamics establishes a nonlinear vibration equation for the flexible printed electron web under multiphysics conditions. The discrete nonlinear vibration equation of state space equation was obtained by the Bubnov–Galerkin method. Utilizing the Runge–Kutta technique of the fourth-order, Poincare maps, phase-plane diagrams, power spectra, bifurcation graphs, and time history diagrams of the moving flexible printed electron web were obtained. The influences of the velocity, electrostatic field, magnetic induction intensity, and follower force on the flexible printed electron web were analyzed. In addition, the Ansoft Maxwell finite element simulation software was used to simulate the magnetic field distribution of the moving web during roll-to-roll transmission. This paper determines the stable working range of the moving flexible printed electron web, which provides a theoretical basis for the preparation of flexible printed electronic webs.