Vibrations of axially moving viscoelastic plate with parabolically varying thickness

Based on the two-dimensional viscoelastic differential constitutive relation, the differential equation of motion of the axially moving viscoelastic rectangular plate constituted by the Kelvin–Voigt model with parabolically varying thickness in the y-direction is derived. The dimensionless complex frequencies of axially moving viscoelastic plate with different boundary conditions versus the dimensionless moving speed for various aspect ratio, thickness parameter and the dimensionless delay time are analyzed by the differential quadrature method. The effects of various parameters such as aspect ratio, thickness parameter, the dimensionless moving speed and the dimensionless delay time on the vibration characteristics of the axially moving viscoelastic rectangular plate with parabolically varying thickness are discussed.