Circular and annular plates are widely used in machinery as basic components. Their torsional vibration behaviour is studied in the paper. An analytical model is developed and the natural frequencies and mode shapes are calculated for the torsional vibration under different boundary conditions. Results show that the torsional vibration behaviour of circular and annular plates is different compared with that of circular shafts. The torque moment in annular plates is transmitted via ring layers from the inner ring to outer ring and vice versa. In addition, the torsional vibration magnitude in terms of the angular displacement decreases with increasing radius. This can be explained by the fact that when the vibration energy is transmitted from the inner ring to outer ring, the circle becomes larger and the energy density becomes lower.
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