Vibration of a moving web with intermediate supports by a P-type method

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Journal of Vibration and Shock ›› 2021, Vol. 40 ›› Issue (8) : 230-236.

YING Shudi1， WANG Yan2， WU Jimei1, 3， WU Qiumin3

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Abstract

The substrate material of Beiren PRC250 printing machine is web of the weight of 200-300 g/m2, the supporting roller in the multi-color printing process was used as the intermediate support. In this paper, a new P-type higher order differential quadrature method was proposed to solve the vibration of a moving web with intermediate supports. According to the Hamilton principle, the energy expression of the moving web was deduced, the shape function of the element was generated by the interpolation of the newly constructed C1 element. The influence of intermediate support and velocity on transverse vibration of the moving web was analyzed. The results show that complex frequency of the paper tape increases with the setting of the intermediate support, and the stable region becomes smaller with the increase of the speed under the constraint of the simple support and the opposite side free movement. The comparative was carried out by the CAE software, and it is proved that the new method to solve the vibration of the intermediate support moving paper tape is better than finite element software.

Key words

moving web / intermediate support / new P-type higher order differential quadrature method / Beiren PRC250

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YING Shudi1， WANG Yan2， WU Jimei1, 3， WU Qiumin3. Vibration of a moving web with intermediate supports by a P-type method[J]. Journal of Vibration and Shock, 2021, 40(8): 230-236

References

［1］WU J M, SHAO M Y,WANG Y,et al. Stability analysis of moving printing web with sine half-wave variable density based on differential quadrature method［J］. Journal of Vibration and Acoustics，2017,139(6)：061018.
［2］SHAO M Y, WU J M, WANG Y,et al. Vibration characteristics for moving printing membrane with varible density along the lateral direction［J］. Shock and Vibration, 2017(4)：1-10.
［3］BANICHUK N, JERONEN J, NEITTAANMKI P. Theoretical study on travelling web dynamics and instability under non-homogeneous tension［J］. International Journal of Mechanical Sciences, 2013, 66：132-140.
［4］武吉梅, 邵明月, 王砚, 等. 具有运动速度的印刷纸板的稳定性分析［J］. 振动与冲击, 2018, 37(8):213-217.
WU Jimei, SHAO Mingyue, WANG Yan, et al. Stability analysis of the printing cardboard with moving speed［J］. Journal of Vibration and Shock,2018, 37(8):213-217.
［5］邵明月, 武吉梅, 王砚, 等. 随从力作用下运动薄膜的非线性强迫振动特性研究［J］. 振动与冲击, 2020, 39(10):215-219.
SHAO Mingyue, WU Jimei, WANG Yan, et al. Nonlinear forced vibration characteristics of membrane subjected to follower force［J］. Journal of Vibration and Shock,2020,39(10):215-219.
［6］NGUYEN Q C, HONG K S. Stabilization of an axially moving web via regulation of axial velocity［J］. Journal of Sound and Vibration, 2011, 330(20)：4676-4688.
［7］王砚, 王忠民. 线性变厚度粘弹性矩形板在随从力作用下的动力稳定性［J］. 固体力学学报, 2008, 29(1)：41-51.
WANG Yan, WANG Zhongmin. Dynamic stability of a linearly varying-thickness viscoelastic rectangular plate subjected to follower force［J］. Chinese Journal of Solid Mechanics, 2008, 29(1)：41-51.
［8］ALIDOOST H, REZAEEPAZHAND J. Instability of a delaminated composite beam subjected to a concentrated follower force［J］. Thin-Walled Structures,2017,120：191-202.
［9］YANG W, XING Y F, LIU B. Analysis of isotropic and composite laminated plates and shells using a differential quadrature hierarchical finite element method［J］. Composite Structures, 2018,205:11-25.
［10］LIU C Y, LIU B, ZHAO L,et al. A differential quadrature hierarchical finite element method and its applications to vibration and bending of Mindlin plates with curvilinear domains［J］. International Journal for Numerical Methods in Engineering, 2017,109(2):174-197.
［11］WU Y, XING Y F,LIU B. Hierarchical p-version C1 finite elements on quadrilateral and triangular domains with curved boundaries and their applications to Kirchhoff plates［J］. International Journal for Numerical Methods in Engineering, 2019,119(3):177-207.
［12］徐芝伦. 弹性力学:下［M］. 北京：高等教育出版社, 2006.