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

Abstract

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.