Nonlinear vibration characteristics and stability of the printing moving membrane

Abstract

Most studies on the membrane vibration are limited to discussing small deflection linear problems, but rarely on the study of nonlinear large deflection problems. In practice, however, membrane deflection is not necessarily far less than the thickness, so it is necessary to research the large deflection vibration problems of moving membrane. In this paper, the large deflection vibration characteristics and stability of the moving printing membrane are analyzed. Large deflection vibration equation of an axially moving membrane is derived by using Von Karman nonlinear plate theory. The large deflection vibration of rectangle moving membrane with four edges fixed boundary is studied by using the Bubnov–Galerkin method which is a semi-analytical-weighted residual method, and the large deflection vibration complex frequency curves along with the change of speed and aspect ratio in the different initial conditions are obtained. The results show that the large deflection nonlinear vibration can be effectively avoided by increasing membrane aspect ratio and decreasing the membrane dimensionless velocity. The study provides theoretical basis for improving the operation stability of the printing equipment.