Multi-Scale Analysis Of Transverse Vibrations Of Axially Moving Thin Plate

The free and forced vibrations of axially moving plate on simple supports are studied in this thesis. The modeling, deriving and numerical analysis are proposed. The method of multiple scales is used to study the vibrations. The main contents include:Firstly, the mathematical modeling of the axially moving thin plate is created considering the nonlinear contributions caused by large deformations. The additional axial forces are introduced on x and y directions. The nonlinear partial differential equations for the axially moving thin plate are derived and the dimensionless terms are used to simplify the final equations.Secondly, the Galerkin method is applied to truncate the partial differential equations into ordinary differential equations for the axially moving plate on simple supports. The natural frequencies for the linear case are discussed. The contributions of axial loading, speed and aspect ratio are provided by numerical examples. The method of multiple scales is used to investigate the effect of nonlinear terms on natural frequencies.Finally, the prime resonance and subresonance of forced vibrations of axially moving thin plate are studied by the method of multiple scales. The frequency-amplitude responses are illustrated by numerical examples.