Transverse Forced Nonlinear Vibration of the Printing Membrane under a Linear Tension Distribution

Geometrically nonlinear vibration characteristics of large deflection of a printing membrane under a linear tension distribution and external excitation are analyzed. The mathematical model of the printing membrane under nonuniform tension is established. Based on the D'Alembert principle and von Karman nonlinear plate theory, the forced nonlinear partial differential equations of the printing membrane under nonuniform tension are deduced. The Galerkin method is applied for discretizing the governing equations, and the method of multiple scales is employed to determine the solution of the ordinary differential equations. The influence of the aspect ratio and the tension ratio on the system stability is highlighted. The results show that nonlinear vibration of the printing membrane can be suppressed by increasing the aspect ratio and reducing the tension ratio in the actual production process.