Dynamic instability of axially moving viscoelastic plate

This paper is devoted to the investigation of the transverse vibration and dynamic stability of the axially moving viscoelastic plate with two opposite edges simply supported and other two opposite edges with simply supported or free. By considering the Kelvin-Voigt model of viscoelasticity, the equation of motion of the plate is derived. The normalized power series method is employed to obtain the complex eigen equations for the axially moving viscoelastic plate. The variation relationship between the first three complex frequencies of the system and the dimensionless axially moving speed with different aspect ratio and dimensionless delay time are analyzed. The results show that the dimensionless delay time, axially moving speed as well as the aspect ratio have remarkable effects on dynamic behaviors and stability of the axially moving viscoelastic plate.