Vibration characteristic analysis and numerical confirmation of an axially moving plate with viscous damping

In this paper, the vibration characteristics of axially moving plates with viscous damping are analyzed. A partial differential linear equation of motion with four simply supported edges is presented. The effects of two different viscous damping models are highlighted, while both of them have been introduced in previous studies. The investigation into the two different viscous damping models is interesting in itself. It is noteworthy that which model is closer to the fact, for which there are no systematic techniques of investigation to deal with this problem. In order to give a reference for possible verification in experiment, the difference of the two different viscous damping models in theory was proposed. The complex frequencies and its corresponding complex modes are studied by the complex mode approach. As other parameters are fixed, the effect of some parameters, such as viscous damping coefficients, axial speeds, aspect ratios, stiffness ratios, and support stiffness parameters, on the frequencies and critical speeds are examined. The complex modes illustrated in the 3-demensional figures are neither symmetric nor anti-symmetric to the midpoint of the plate owing to the plate motion. The differential quadrature scheme is used to verify the modes for the first time. The numerical calculations confirm the analytical results.