WU Ji-mei, JING Tao, WANG Yan, LI Yan-feng, XUE Zhi-cheng, WU Qiu-min. Transverse Vibration Control of Moving Printing Membranes With Bending Stiffness[J]. Applied Mathematics and Mechanics, 2015, 36(7): 686-699. doi: 10.3879/j.issn.1000-0887.2015.07.002
 Citation: WU Ji-mei, JING Tao, WANG Yan, LI Yan-feng, XUE Zhi-cheng, WU Qiu-min. Transverse Vibration Control of Moving Printing Membranes With Bending Stiffness[J]. Applied Mathematics and Mechanics, 2015, 36(7): 686-699.

# Transverse Vibration Control of Moving Printing Membranes With Bending Stiffness

##### doi: 10.3879/j.issn.1000-0887.2015.07.002
Funds:  The National Science Foundation of China (11172056); The National Basic Research Program of China(973 Program)(2014CB046803)
• Received Date: 2014-12-02
• Rev Recd Date: 2015-04-13
• Publish Date: 2015-07-15
• The active control of transverse vibration of axially moving rectangular membranes with bending stiffness was investigated during the printing process. A computing model for the moving printing membrane with bending stiffness was established. The discretized dynamic equations for the moving membrane were obtained with the finite difference method, and the state equations of the transverse vibration control system for the moving membrane were derived. The suboptimal control method was applied to conduct the active control of transverse vibration of the moving membrane under various boundary conditions of actual printing processes. The calculated results show that the vibration of the moving rectangular membrane can be controlled effectively within a short time with the suboptimal vibration control method. The control effect will be better when the actuators act on some fixed nodes with 4 edges simply supported; when the actuators act on variable nodes, the control effect will be the best in the case of central point actuation under the 2 types of boundary conditions, where the dimensionless time of velocity attenuation to zero is shorter than those in the other cases of actuation at the rest nodes. It is indicated that the transverse vibration of axially moving rectangular membranes can be controlled effectively with the suboptimal control method, thus the printing precision can be promoted and the printing quality ensured.
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