Vibration Characteristics Of Axially Moving Beams And In-Plane Translating Plates

The axially moving structures, as models for a variety of mechanical engineering components, are widely applied in nature, real life, engineering and other fields. It includes power transmission belt, elevator cable lifts, saw blades, textile fibers, conveyor belts, tapes, audio tapes, etc. Owing to variations in axially moving speed, the axially moving structures have large transverse vibrations. Therefore, the study of the transverse vibration of the axially moving structures have great significances.The axially moving beam and the in-plane translating plate are researched in this paper, respectively. The dynamic models are established. The theoretical analysis and numerical validation are used to research vibration characteristics of the axially moving beam and the in-plane translating plate. The main contents are divided as follows:In chapter 2, the parametric and 3:1 inner resonances of axially moving viscoelastic beams are researched. The longitudinally varying tension is introducd. The generalized Hamilton principle is usd to establish the governing equations and the associated boundary conditions. The effects of the nonhomogeneous boundary conditions owing to the viscoelasticity are highlighted. The method of multiple scales is used to establish the solvability conditions. The nonlinear steady-state oscillating response along with the stability and bifurcation of the beam is investigated. The influence of the elastic foundation, limited support stiffnesses, influence of viscoelastic coefficients and viscous damping coefficients are considered for the parametric resonance and 3:1 inner resonances. The numerical calculations by the differential quadrature scheme are used to verify the approximate analytical results.In chapter 3, the vibration characteristics of axially moving plates under the effect of longitudinally varying tension are researched. The generalized Hamilton principle is used to establish the partial differential equations the associated boundary conditions. The effects of two different viscous damping models are highlighted. The complex mode method is employed to analyze the complex frequencies and its corresponding complex modes. The effect of viscous damping coefficient, axial velocity, aspect ratios, stiffness ratios and bearing stiffness on the natural frequencies and the critical speeds are considered. The numerical calculations by the differential quadrature scheme are used to verify the analytical results.In chapter 4, the dynamic stability of axially accelerating viscoelastic plate with longitudinally varying tensions and non-homogeneous boundary conditions are analyzed. Summation and principal parametric resonances are researched. The generalized Hamilton principle is applied to get the governing equations of coupled planar vibration and the associated boundary conditions.The method of multiple scales is used to establish the solvability conditions.The impacts of viscoelasticity coefficient, viscous damping coefficient and other parameters on the stable boundary are investigated, respectively. The numerical calculations of the differential quadrature scheme are used to confirm the results of the approximate analytical solution.