Vibration Analysis Of Moving Thin Plate In Boundary Layer

On the basis of the Kirchhoff hypothesis, the dynamics equation of the axially moving thin plate with inertial and geometrical nonlinearities up to the third order is derived through using Kane's equation and Rayleigh-Ritz method. In a simply supported case, the transverse vibration of the thin plate excited by the support motion is analyzed with consideration of the first natural mode of the simply supported plate. The relationship between the natural frequencies and the moving acceleration of the thin plate are obtained numerically.In order to give better insight into the vibration of moving thin plate, consequently, the effect of boundary layer on the natural vibration of the thin plate is studied. Based on the Kirchhoff hypothesis, the dynamics model of the thin plate are established by using the ideal boundary layer theory, and a two-roll nip model is considered herein. For small transverse vibration, the equation of motion with boundary layer is obtained. According to the assumed shape of the boundary layer, the boundary layer thickness is calculated, and the additional mass due to the viscous flow is also determined. The natural frequencies with boundary layer versus moving speed are obtained by using FEM method. The results show that it is need to consider the effect of boundary layer on the vibration of thin plate as the thin plate moving in air.