Thermoelastic Coupling Vibration and Stability Analysis of Rotating Annular Sector Plates

Abstract

This study investigates the thermoelastic coupling vibration and stability of rotating annular sector plates. Based on Hamilton's principle and thermal conduction equation with deformation effect, the differential equation of transverse vibration for a rotating annular sector plate is established. The differential equation of vibration and corresponding boundary conditions are discretized by the differential quadrature method. Then, the thermoelastic coupling transverse vibrations under three different boundary conditions are calculated. The change curve of the first three order dimensionless complex frequencies of the rotating annular sector plate with the dimensionless angular speed are analyzed in the case of the thermoelastic coupling and uncoupling. The effects of the dimensionless angular speed, the ratio of inner to outer radius, the sector angle, and the dimensionless thermoelastic coupling coefficient on transverse vibration and stability of the annular sector plate are discussed. Finally, we obtained the type of instability and corresponding critical speed of the rotating annular sector plate in the case of the thermoelastic coupling and uncoupling.