Nonlinear vibration of moving orthotopic films under oblique support. (English) Zbl 1535.74282
Summary: To reduce product damage caused by the vibration instability phenomenon associated with the commutation of new material films during long-path transportation, the nonlinear vibration of orthotropic films transported under oblique support is investigated. First, on the basis of von Karman’s large deflection theory and D’Alembert’s principle, then through coordinate system transformation, the vibration partial differential equations of the system in an oblique coordinate system are established, taking into account the influence of damping. Next, the equations are discretized by the Galerkin method to obtain the system’s nonlinear vibration ordinary differential equations. Finally, the fourth-order Runge-Kutta method is used to carry out numerical calculations of the system to analyze the effects of the oblique support angle, orthotopic coefficient, and damping on the nonlinear vibration of films in transportation. The research results show that the selection of these three important parameters has an impact on the vibration characteristics of moving orthotopic films, and reasonable suggestions are made based on the parameter range for the stable motion of the system, which will help in structural adjustment and stability control during actual printing and manufacturing.
MSC:
| 74H45 | Vibrations in dynamical problems in solid mechanics |
Keywords:
moving orthotopic films; oblique support; nonlinear vibration; fourth-order Runge-Kutta methodReferences:
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