Abstract
The study investigates the forced nonlinear vibration characteristics of an axially moving printing paper web with variable density in the lateral direction. The nonlinear governing equations of the web can be obtained by the von Karman large deflection thin plate theory. The vibration equations are discretized using the Bubnov–Galerkin method. The fourth-order Runge–Kutta technique is used to solve the differential equations of the nonlinear system. The phase-plane diagrams, time histories, bifurcation graphs, Poincare maps, and power spectrum are employed to analyze the influence of density coefficient, velocity, and aspect ratio on the nonlinear dynamic behavior of the moving paper web. The stable working region and the divergence instability region of the web are obtained. The research provides a theoretical foundation for improving the dynamic stability of a moving paper web.
Highlights
In printing, the surface density of a printing web corresponding to each printout is different
The ink and fountain solution used during the printing process will affect the density of the web surface, and the uneven thickness of the substrate will change surface density, the vibration characteristics of printing webs will change, and in this manner, the web is prone to wrinkling, tearing, and surface scratches; as a result, the overprint accuracy and printing quality will reduce.[1]
Chen et al.[5,6,7] systematically studied the nonlinear vibration characteristics of axially moving viscoelastic strings based on the fourth-order Galerkin truncation and the method of multiple scales
Summary
The surface density of a printing web corresponding to each printout is different. Keywords Nonlinear forced vibration, variable density, moving paper web, fourth-order Runge–Kutta technique Chen et al.[5,6,7] systematically studied the nonlinear vibration characteristics of axially moving viscoelastic strings based on the fourth-order Galerkin truncation and the method of multiple scales.
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