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.

Stability of an Axially Moving Flexible Cantilevered Plate in an Axial Flow

When a flexible plate of machines and structures is in axial flow, increasing the flow velocity induces the dynamic instability. Also, the similar instability occurs for a thin film wound to a coil form and a band saw driven with high transport speed even if we consider there is no effect of fluid. However, if a flexible plate is very light, and the rigidity is weak, the dynamic instability of a plate is thought to be affected both by the transport speed of plate and by the surrounding fluid. In this paper, the stability analysis is performed using the velocity potential based on the boundary conditions between the surrounding fluid and the plate. The numerical studies are performed as for a cantilevered plate. The case of an axially moving plate in a still fluid, the case of a stationary plate subjected to an axial flow, and the case of an axially moving plate in neglecting the effect of surrounding fluid are examined. And, the effect of the transport speed of cantilevered plate on the dynamic stability is discussed. Furthermore, another stability analysis is also performed by using the non-circulatory aerodynamic theory, and the numerical analysis results are examined and discussed.