Stability Analysis of Moving Printing Web With Sine Half-Wave Variable Density Based on Differential Quadrature Method

2017 ◽  
Vol 139 (6) ◽  
Author(s):  
Jimei Wu ◽  
Mingyue Shao ◽  
Yan Wang ◽  
Qiumin Wu ◽  
Fan Zhao
Keyword(s):  
Flexible Electronics ◽  
Transverse Vibration ◽  
Differential Quadrature Method ◽  
Variable Density ◽  
Differential Quadrature ◽  
Printing Press ◽  
Quadrature Method ◽  
Half Wave ◽  
The Impact ◽  
Density Coefficient

The moving web is widely used to make printing and packaging products, flexible electronics, cloths, etc. The impact of the variable density on printing web dynamic behavior is considered. The density changes in the form of sine half-wave in the lateral direction. Based on the D'Alembert's principle, the transverse vibration differential equation of moving printing web with variable density is established and is discretized by using the differential quadrature method (DQM). The complex characteristic equation is derived. The impacts of the density coefficient and the dimensionless speed on the web stability and vibration characteristics are discussed. The results show that it is feasible to use the DQM to analyze the problem of transverse vibration of printing web with varying density; the tension ratio and the density coefficient have important impacts on the stability of moving printing web. This study provides theoretical guidance and basis for optimizing the structure of printing press and improving the stable working speed of printing press and web.

scholarly journals Vibration Characteristics for Moving Printing Membrane with Variable Density along the Lateral Direction

2017 ◽  
Vol 2017 ◽  
pp. 1-10 ◽  
Author(s):  
Mingyue Shao ◽  
Jimei Wu ◽  
Yan Wang ◽  
Qiumin Wu ◽  
Yuan Chen
Keyword(s):  
Density Distribution ◽  
Transverse Vibration ◽  
High Speed ◽  
Differential Quadrature Method ◽  
Variable Density ◽  
Vibration Characteristics ◽  
Lateral Direction ◽  
Vibration Model ◽  
The Stability ◽  
Density Coefficient

The vibration model of moving membrane with variable density distribution is established, and the density distribution of the moving membrane varies along the lateral direction. The transverse vibration differential equations of moving membrane are established based on D’Alembert’s principle and discretized by using the differential quadrature method (DQM). The relationships of the first three dimensionless complex frequencies between dimensionless speed, density coefficient, and tension ratio of the membrane are analyzed by numerical calculation. The effects of the density coefficient and the tension ratio on transverse vibration characteristics of the membrane are investigated. The relationship between density coefficient and critical speed is obtained. The numerical results show that the density coefficient and the tension ratio have important influence on the stability of moving membrane. So the study provides a theoretical basis for improving the working stability of the membrane in the high-speed printing process.

Free transverse vibration analysis of thin rectangular plates locally suspended on elastic beam

2012 ◽  
Vol 227 (7) ◽  
pp. 1515-1524 ◽  
Author(s):  
M Golkaram ◽  
MM Aghdam
Keyword(s):  
Transverse Vibration ◽  
Plate Theory ◽  
Rectangular Cross Section ◽  
Differential Quadrature Method ◽  
Differential Quadrature ◽  
Rectangular Plates ◽  
Quadrature Method ◽  
Generalized Differential Quadrature Method ◽  
Free Transverse Vibration ◽  
Generalized Differential

Free transverse vibration of thin rectangular plates locally suspended on deformable beam is presented using generalized differential quadrature method. The plate is completely free at all edges except a local region which is attached to a thin beam with rectangular cross section. The other side of the beam is fixed and the whole system is subjected to free transverse vibrations. According to classical plate theory and Euler–Bernoulli beam assumption, two coupled partial differential equations of the system are obtained. The governing equations and solution domain are discretized based on the generalized differential quadrature method and natural frequencies of the plate attached to the beam are obtained. Accuracy of the predictions is investigated using four simplified cases which show reasonably good agreement. For the general case, however, due to lack of data in the literature, predictions are compared with finite element results, which also demonstrate close agreement.

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