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Analytical Study on Torsional Vibration of Circular and Annular Plate

Abstract Circular and annular plates are widely used in machinery as basic components. Their torsional vibration behaviour is studied in this article. An analytical model is developed, and the natural frequencies and mode shapes are calculated for the torsional vibration under different boundary conditions. A physical insight is gained into the torsional vibration behaviour of circular and annular plates. Results show that the torsional vibration behaviour of circular and annular plates is different compared with that of circular shafts. Torque moment in annular plates is transmitted via ring layers from the inner ring to the outer ring and vice versa. In addition, the torsional vibration magnitude in terms of angular displacement decreases with increase in radius. This can be explained by the fact that, when vibration energy is transmitted from the inner ring to the outer ring, the circle becomes larger and the energy density becomes lower. It is similar to the situation of a spherical wave propagation from its source. The analytical results are verified using an FEA model. Good agreement is shown between the analytical and FEA models.