Based on classical plate theory, standard and spectral finite element methods are extended for vibration and dynamic stability of axially moving thin plates subjected to in-plane forces. The formulation of the standard method earned through Hamilton’s principle is independent of element type. But for solving numerical examples, an isoparametric quadrilateral element is developed using Lagrange interpolation functions. The spectral method is, in fact, the solution of motion equation for an axially moving plate. Although this method has some limitations concerning boundary condition of plate and in-plane forces, it leads to an exact solution of free vibration and stability of plates travelling on parallel rollers. The method can be used as a benchmark of accuracy of other numerical methods.

Keywords: Axially moving plate, Finite element, Spectral finite element method, Vibration, Stability, Exact solution, Lagrange functions

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