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.
Highlights
As a basic structure, the annular sector plate has been widely used in practical engineering, such as missiles, ships, instruments, and machine structures
This study investigates the thermoelastic coupling vibration and stability of rotating annular sector plates
This study aims to construct the differential equation of thermoelastic coupling transverse vibration of the rotating annular sector plate based on Hamilton’s principle and the thermal conduction equation
Summary
The annular sector plate has been widely used in practical engineering, such as missiles, ships, instruments, and machine structures. The behavior of annular sector plate is very important for these structures, which has attracted great attention from many researchers. Some research work has been done on the bending behavior of the annular sector plate. Jomehzadeh et al and Sahraee [1, 2] analyzed the bending of functionally graded annular sector plates based on the Levinson plate theory and the first order shear deformation plate theory. Qian and Yan [4] studied the bending problems of thin elastic annular sector plate with supported along radial edges and free along circular edges by a solution of deflection in the form of Fourier-Bessel double series
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