Dynamical Analysis Of Transverse Vibrations Of Axially Moving Thin Plate

The transverse vibration of the axially moving rectangle thin plate is studied in this thesis. The perturbation method is used to investigate the nonlinear free and parametric vibrations of the system and some numerical examples are presented to highlight the conclusions.Firstly, the governing partial differential equation is derived by considering only the transverse deformation of the axially moving plate based on the nonlinear constitutive relation. The natural frequencies and vibration modes are analyzed for three types of supporting conditions, namely, SSSS, CCCC, and SCSC, where S stands for simple support and C for clamped support. The contributions of some parameters such as axially moving speed and ratio of length and width are presented by some numerical examples.Secondly, the Galerkin method is used to transform the governing partial differential equations into a set of ordinary differential equations. Via averaging method, the subharmonic and combination resonances are discussed based on the fact that the axially moving speed is an addition of mean velocity and a small periodic oscillation.Finally, the free and parametric nonlinear vibrations are studied by the method of multiple scales. The nonlinear natural frequencies are calculated for different boundary conditions. The steady state amplitude-frequency response of accelerating axially moving plate is investigated.