| Summary: | The thesis is divided into two parts. Part I describes a new electro-optical method of recording accurately the whirling vibrations of a vertical, centrally loaded shaft under laboratory conditions. The design and analysis of a novel type of regulator is given: this maintains a high degree of calibration accuracy despite short-term and long-term changes of illumination and photocell characteristics. The automatic measurement of shaft speed and frequency by electronic counter and master clock is described; and an electromagnetic method of exciting transverse vibration under small applied loads. In Part II, following a short historical review of the literature, so-called ideal conditions are criticised, particularly as applied.to the assumption of constant shaft speed independent of the characteristics of the prime-mover, and to the practical uncertainty of the exact nature of the end-fixings. Experiments on the natural frequency of transverse vibration under various conditions are described, and the bearings used shown to be a close approximation to free-free fixings. The simple equations of the system are derived and theoretical curves given of amplitude and phase, including a case of non-linear damping. Experimental measurements are compared. Experiments disclose the existence of sub-critical and hyper-critical instability when the torque-speed characteristic of the driving motor is poor. The hypercritical instability or runaway, is simply explained: the sub-critical instability is analysed by deriving the differential equations of the system in full and inserting the initial conditions and the characteristic of the driving motor. These equations are non-linear and their solution is carried out on an analogue computer, although the nature of the equations militates against an accurate result. Experiments are carried out to show that partial suppression of the dangerous vibration in the region of the critical speed may be obtained by means of bearings possessing a non-linear profile and giving rise to a restoring force of the form (ax + bx3), x being the deflection. The form of the response is in accordance with the solution of Duffing's equation and exhibits the 'jump' phenomenon. Several points of detail and a qualitative analogue of a variable stiffness system are discussed in appendices.
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