Vibration characteristics and stability of mass-added coated polyethylene film under the follower force

The vibration characteristics and stability of mass-added coated polyethylene films under follower force using the differential-integral method are investigated in this paper. Unlike previous studies on film vibration characteristics, this paper considers a coated PE film system with continuously increasing mass (mass increase, with a rate of change of mass greater than zero over time). Firstly, a mechanical model of the mass-added coated PE film under follower force is established. Secondly, based on Hamilton’s principle, the control differential equation for the vibration of the mass-added coated PE film is derived and made dimensionless. Then, the dimensionless control equation and boundary conditions are discretized using the differential-integral method to obtain the characteristic equation. Finally, the results are compared with existing literature data to verify the applicability and accuracy of the differential-integral method. The effects of flow rate, coating time, follower force on film stability are analyzed under four-sided fixed and opposite-sided fixed/opposite-free conditions.