NONLINEAR FREE VIBRATION CHARACTERISTICS OF PRINTING PAPER WEB WITH VARIABLE DENSITY

Abstract

Most studies on the vibration of variable density paper web are limited to the discussion of small deflection linear problems. There are few researches on nonlinear vibration problems with large deflection in variable density printing web.However,in practice,the density of the web is varied due to the difference in the distribution of the printed image. In this paper,the nonlinear vibration characteristics of moving printing web with variable density are studied. Based on the von Karman plate theory,the vibration equation of the large deflection motion of the axially moving paper is deduced. The differential equation is divided by the Bubnov-Galerkin method,and the differential equation is solved by elliptic integral method. The frequency expression of the nonlinear vibration is obtained. The influence of density coefficient,dimensionless velocity and aspect ratio on the complex frequency of large deflection vibration of moving paper under different initial conditions is analyzed. This study provides a theoretical basis for improving the stability of printing equipment.

Keywords

• Nonlinear vibration;Variable density;Printing paper web;Bubnov-Galerkin method