The dynamic analysis and control of cracked rotating beams

This thesis covers the dynamic modelling of un-cracked and cracked rotating beams. Accordingly, a new model of a rotating cracked beam is developed using the finite element and the Rayleigh-Ritz method to characterise and analyse its dynamic behaviour. The effect of various parameters are investigated, such as rotational speed, hub ratio and slenderness ratio. In addition, the critical speed, buckling speed and veering phenomena are identified. The numerical results produced are shown to be in good agreement with models based on finite element representations. In addition to the theoretical investigations, experimental validation is presented. A test rig was designed and manufactured with a changeable rotating hub mount for different test requirements. Moreover, the rig was conceived to incorporate capabilities such as applying variable rotational speed using a variable frequency driver and provide vertical base excitation input to the centre of rotation of the hub. The tests were performed using random excitation at the root of the rotating cantilever beam to excite the flapwise modes of the beam. The responses were then measured optically using a high-speed camera, and the images were post-processed using a digital image correlation (DIC) method. This non-invasive optical method was used to extract the temporal deflection of the beam. The frequency response functions are then obtained from the measured responses. The estimated modal frequencies were compared with numerical simulations to validate the Rayleigh-Ritz and FE numerical models at various rotational speeds. Furthermore, an experimental crack detection was implemented and the results showed a good match to the introduced actual crack location and depth. The crack detection approach on the rotating cracked beam uses the fundamental and second natural frequencies. For vibration control of the rotating beam, a real-time velocity feedback control was applied using a remote single optical high-speed camera. An electromagnetic actuator was designed and mounted on the rotating hub to apply a feedback force on the rotating beam. The results for vibration control of the rotating beam show significant active damping and reduction in the amplitude of the first resonance over a wide range of rotational speeds.