The Nonlinear Resonance Of Axially Moving Thin Plate Under Linera Load

The axially moving structure exists widely in our lives and actual engineering projects.Such as power transmission belt, elevator, saw blades, magnetic tape, rolling plate etc.More and more researchers have paid much attention to axially moving structure at homeand abroad, there is very important practical significance to study the nonlinear vibrationof axially moving structure. This thesis mainly uses the theoretical derivation andnumerical calculation to analyze the main resonance, sub harmonic resonance and superharmonic resonance behavior of axially moving thin plate.Considering geometric nonlinear, based on the theory of large deflection, theexpressions of total kinetic energy, potential energy and external force virtual work areobtained. The nonlinear vibration equations of axially moving thin plate are derived byusing Hamilton principle.Considering the axially moving strip thin plate simply supported on two opposite edgeswhich is subjected to linear load, by using the Galerkin method and multiple-scale method,the amplitude-frequency equations of the main resonance, sub harmonic resonance andsuper harmonic resonance behavior of the system are obtained. Numerical simulation ofthe above three kinds of resonance, amplitude-frequency characteristic curves and therelation of resonance amplitude and other physical parameters are obtained by usingMatlab when the system is subjected to a single excitation force. The influence ofdetuning parameter, axial speed, excitation amplitude, thickness and the position ofharmonic exciting force on the dynamic characteristics are investigated. And consideringsystem which is subjected to two excitation forces, the influence between the forcesdistance and the amplitude on the dynamic characteristics are investigated when systemhappens the above three kinds of resonance.Numerical simulation of primary resonance, super harmonic resonance and subharmonic resonance of the moving rectangular thin plate simply supported on twoopposite edges which is subjected to linear load, using Matlab to plot the time historydiagram, phase diagram and Poincaré map time of the system. The influences of the axial speed and excitation amplitude on the dynamic characteristics are investigated.