Natural frequencies determination of axially moving viscoelastic plates based on first-order shear deformation theory

In this paper, the natural frequencies of a thin axially moving viscoelastic plate have been calculated analytically based on the first-order shear deformationtheory. The plate translates axially along the longitudinal direction with a constant velocity between two pairs of rollers and it is subjected to a uniformtension at the both ends. The equations of motions, which are a system of partial differential equation, have been derived by using the Hamilton principle. It isassumed that the deflection of the plate and aspect ratio of b/L be small. The behavior of the viscoelastic plate has been defined with a three-parameter Zener model inshear and elastic in bulk. The wave solution method has been used to extract the natural frequencies from theequations of motions. Finally, a parametric study has been performed to investigate the effects of the translating speed, thickness and viscoelastic propertieson the natural frequencies of the structure. The effects of above- mentioned parameters on the first-four naturalfrequencies have been shown in the diagrams. The numerical results showed that the translating speed and thickness of the moving plate have no significant effecton first-four natural frequencies. Also, all frequencies are independent of E1 for E1<109.

کلیدواژه ها:

Natural frequency ، Viscoelastic ، Moving plate ، Shear deformation theory ، Wave solution ،