Equilibrium and buckling stability for axially traveling plates

The methodology is presented in this paper through investigation of the equilibrium and stability of thin plate axially traveling with high-speed, which is applicable for traveling plate and shell structures. Equilibrium, membrane forces and buckling stability for the steady state motion of axially traveling, thin plates are obtained analytically. The equilibrium solutions and membrane forces for a single mode are discussed as a sample. The transverse displacement amplitude and the buckling stability are presented. The results are reducible to the linear, von Karman and nonlinear membrane theories. Finally, the application range of those analytical results is discussed. Such an investigation provides some useful results for numerical simulations and engineering design. For higher modes, the nonlinear plate theory should be used even if the deflection amplitude is very small compared to plate thickness.