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. doi: 10.3879/j.issn.1000-0887.2015.07.002

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.
  • loading
  • [1]
    Altunsaray E, Bayer I. Deflection and free vibration of symmetrically laminated quasi-isotropic thin rectangular plates for different boundary conditions[J]. Ocean Engineering,2013,57: 197-222.
    [2]
    YU Tian-chong, NIE Guo-jun, ZHONG Zheng, CHU Fu-yun. Analytical solution of rectangular plate with in-plane variable stiffness[J]. Applied Mathematics and Mechanics(English Edition),2013,34(4): 395-404.
    [3]
    唐有绮, 陈立群. 面内平动黏弹性板非线性振动的内-外联合共振[J]. 应用数学和力学, 2013,34(5): 480-487.(TANG You-qi, CHEN Li-qun. Internal-external combination resonance of nonlinear vibration of in-plane translating viscoelastic plates[J].Applied Mathematics and Mechanics,2013,34(5): 480-487.(in Chinese))
    [4]
    TANG You-qi, CHEN Li-qun. Stability analysis and numerical confirmation in parametric resonance of axially moving viscoelastic plates with time-dependent speed[J]. European Journal of Mechanics- A/Solids,2013,37: 106-121.
    [5]
    CHEN Li-qun, YANG Xiao-dong. Steady-state response of axially moving viscoelastic beams with pulsating speed: comparison of two nonlinear models[J]. International Journal of Solids and Structures,2005,42(1): 37-50.
    [6]
    CHEN Li-qun, YANG Xiao-dong. Transverse nonlinear dynamics of axially accelerating viscoelastic beams based on 4-term Galerkin truncation[J]. Chaos, Solitons & Fractals,2006,27(3): 748-757.
    [7]
    Kim J, Cho J, Lee U, Park S. Modal spectral element formulation for axially moving plates subjected to in-plane axial tension[J]. Computers & Structures,2003,81(20): 2011-2020.
    [8]
    周银锋, 王忠民. 轴向运动粘弹性板的横向振动特性[J]. 应用数学和力学, 2007,28(2): 191-199.(ZHOU Yin-feng, WANG Zhong-min. The transverse vibration characteristics of the axially moving viscoelastic plate[J]. Applied Mathematics and Mechanics,2007,28(2): 191-199.(in Chinese))
    [9]
    Saksa T, Banichuk N, Jeronen J, Kurki M, Tuovinen T. Dynamic analysis for axially moving viscoelastic panels[J]. International Journal of Solids and Structures,2012,49(23/24): 3355-3366.
    [10]
    Greco D, Blanc P. Active vibration control of flexible materials found within printing machines[J]. Journal of Sound and Vibration,2007,300(3/5): 831-846.
    [11]
    Nguyen Q C, Hong K S. Transverse vibration control of axially moving membranes by regulation of axial velocity[J].IEEE Transactions on Control Systems Technology,2012,20(4): 1124-1131.
    [12]
    Nagarkatti S P, ZHANG Fu-min, Costic B T, Dawson D M, Rahn C D. Speed tracking and transverse vibration control of an axially accelerating web[J]. Mechanical Systems and Signal Processing,2002,16(2/3): 337-356.
    [13]
    Nguyen Q C, Hong K S. Simultaneous control of longitudinal and transverse vibrations of an axially moving string with velocity tracking[J]. Journal of Sound and Vibration,2012,331(13): 3006-3019.
    [14]
    倪振华. 振动力学[M]. 西安: 西安交通大学出版社, 1986: 430-480. (NI Zhen-hua. Vibration Mechanics [M]. Xi’an: Xi’an Jiaotong University Press, 1986: 430-480.(in Chinese))
    [15]
    Johnson T L, Athans M. On the design of optimal constrained dynamic compensators for linear constant systems[J]. Automatic Control, IEEE Transactions on,1970,15(6): 658-660.
    [16]
    Levine W S, Athans M. On the determination of the optimal constant output feedback gains for liner multivariable systems[J].Automatic Control, IEEE Transactions on,1970,15(1): 44-48.
  • 加载中

Catalog

    通讯作者: 陈斌, bchen63@163.com
    • 1. 

      沈阳化工大学材料科学与工程学院 沈阳 110142

    1. 本站搜索
    2. 百度学术搜索
    3. 万方数据库搜索
    4. CNKI搜索

    Article Metrics

    Article views (758) PDF downloads(629) Cited by()
    Proportional views
    Related

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return