The two-dimensional viscoelastic differential constitutive relation is employed in this paper, in order to establish the equation of motion of axially moving viscoelastic rectangular plate. Two boundary conditions are investigated, namely the clamped free and two opposite edges simply supported and two others free. The differential quadrature method is used to solve the resulting complex eigenvalues equation. The influence of boundary conditions on the instability of a moving viscoelastic plate is analyzed firstly, and secondly the effects of system parameters such as plate's viscosity and aspect ratio on the vibration frequencies are presented.
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