Parametric Vibration Stability Analysis of an Axially Moving Plate with Periodical Distributed Materials

BackgroundsThe axially moving structures are commonly seen in the transporting belt, the tracks of heavy engineering vehicles and the manufacturing process. In many practical engineering fields, the material properties of the axially moving structures are not uniform.PurposesThe aim of the present paper is to provide some basic movement rules and stability evidence for the axially moving structures with non-uniformly distributed materials. The present paper investigates the dynamics of an axially moving plate with periodical distributed material properties.MethodsThe equation of motion of the material periodically distributed axially moving plate is established based on the Poisson-Kirchhoff plate theory. The assumed mode method is applied to discretize the equation of motion of the axially moving plate into ordinary differential equations. The Floquet theory is adopted to analyze the stability of the parametric excitation system.ResultsThe effects of the mass density and the elastic modulus of the material on the stability of the system are researched. The effectiveness of the Floquet theory is proved by numerical simulations.ConclusionsFrom the results, the divergence and flutter types of instability of the plate can be observed in a vibration period. The plate is more stable when the material properties are approaching.