The Study For Nonlinear Vibration Of Axailly Moving Rectangular Thin Plate In Rolling Process

With the need for low-cost and high-quality produces increased, prevention ofvibration becomes an increasingly important task in the design and operation of rollingmill in worldwide. The vibration phenomenon of axially moving systems is very commonin daily life，widely used in military, machinery, civil, electronics, aerospace and otherengineering practice. A variety of systems with axially moving such as powertransmission belts, textile fibers, band saw, paper, tapes and the composite materiallaminate of aerospace engineering etc. can be simplified as axially moving plates. Withthe rapid development of modern science and technology, the vibration problem of axiallymoving systems has also been wider attention. Therefore, the study on the vibrationcharacteristics of axially moving systems in the rolling process has important theoreticaland practical significance.In this thesis, the nonlinear vibration of axially moving rectangular thin platessubjected to external excitation in rolling process is studied. Parametric vibration andforced vibration of the axially moving rectangular thin plates in the two opposite endssimply supported and two opposite ends free boundary condition is focused discussed.Firstly, according to the moving classical plate theory and sheet theory, the nonlinearvibration equations of axially moving rectangular thin plates were deduced by usingHamilton’s principle in rolling process.Secondly, based on the setting of the displacement function, substitute thedisplacement solution into the vibration equation which meet the boundary condition oftwo opposite ends simply supported and two opposite ends free, using the method ofGalerkin to integrate it and make it dimensionless, the parametric vibration and forcedvibration differential equation is deduced, and the nonlinear vibration of systemdifferential equations are solved.Finally, the axially moving rectangular thin plates in two opposite ends simplysupported and two opposite ends free boundary conditions were analyzed throughcalculation by matlab programming. In the parametric vibration and forced vibration problems, the time history plot, the phase chart and the poincaré map of the axiallymoving rectangular thin plates with two opposite ends simply supported and two oppositeends free boundary conditions were derived under different parameters. By changing theparameters, by means of calculated example, the influence of different system parameterson nonlinear resonance properties of system, such as load size, speed change, dampingcoefficient and width of plate, were discussed.