Modal spectral element formulation for axially moving plates subjected to in-plane axial tension

The use of frequency-dependent spectral element matrix (or dynamic stiffness matrix) in structural dynamics is known to provide very accurate solutions, while reducing the number of degrees-of-freedom to resolve the computational and cost problems. Thus, in the present paper, the modal spectral element is formulated for thin plates moving with constant speed under a uniform in-plane axial tension. The concept of the Kantorovich method is used to formulate the modal spectral element matrix in the frequency-domain. The present modal spectral element is then evaluated by comparing its solutions with exact analytical solutions as well as with FEM solutions. The effects of the moving speed and the in-plane tension on the dynamic characteristics of a moving plate are investigated numerically.