Nonlinear vibration characteristics analysis of variable density printing moving membrane

A printing moving membrane is studied. The model of the moving membrane with parabolic density is established. Then, the Von-Karman equations expressed by the deflection function and the internal force function of axially moving membrane are derived based on the theory of elasticity. The nonlinear vibration characteristics of the variable density moving membrane under clamped boundary are studied. The time and spatial variables are separated by Bubnov-Galerkin method and the nonlinear vibration frequency expression of the variable density moving membrane is obtained. The relation curves of frequency and density coefficient, velocity, and length to width ratio are obtained. The effects of velocity, length width ratio, density coefficient and initial value of vibration on the nonlinear vibration of printing membranes are discussed.