Dynamic stability of rotating viscoelastic annular sector plate

Abstract

The dynamic characteristics and stability of rotating viscoelastic annular sector plates are investigated. Based on the thin plate theory and the two-dimensional viscoelastic differential constitutive relation, the differential equation of transverse vibration for a rotating viscoelastic annular sector plate in the polar coordinate is established. The membrane forces involving the rotating inertial force in the Laplace domain are solved. The differential quadrature method is used to discretize the differential equation of vibration and corresponding boundary conditions. The generalized eigenvalue under different boundary conditions is calculated, and the change curve of the first three-order dimensionless complex frequencies of rotating viscoelastic annular sector plate with the dimensionless angular speed is analyzed. The effects of the ratio of inner to outer radius, the sector angle, and the dimensionless delay time on transverse vibration and stability of the annular sector plate are analyzed. The type of instability and corresponding critical speed of annular sector plate are obtained.