A novel method of flexible-rotor vibration control, using an active contactless angular electromagnetic actuator is presented. A theoretical comparison of radial and angular damping is performed. Three different performance indices are defined and used to determine controller optimum damping/location data for different shaft systems. The controller settings are determined for two main cases: i) such that only one damping value is allowed throughout the entire shaft speed range (passive or fixed-gain active control), ii) the damping value is controlled as a function of rotor speed (adaptive control). The parameter optimisation, made possible by the creation of a simple but efficient numerical technique employed in conjunction with the transfer matrix method, is restricted to considering a speed range covering the first three rigid-bearing critical speeds for a uniform shaft supported by a variety of bearings. However, the approach is sufficiently general to allow the study of any required speed range. It is shown that for both the radial and angular dampers when mounted at the bearings, there is a definite support stiffness value above which the angular damper is the more efficient, but below which the opposite is true. When the conditions for 'fixed-points' are satisfied, then a simple on-off control strategy can be used effectively employing either type of controller. Angular damping is shown also to be an effective means of suppressing 'oil-whirl' type instability. The theoretical work is supported by experimental investigations on a laboratory rig which is representative of a general flexible rotor system. An electromagnetic controller is mounted at one bearing and the reduction of shaft unbalance response and bearing forces recorded for various conditions. Significant reductions in system synchronous response are observed at running speeds close to the first critical speed when electromagnetic stiffness and/or damping is employed. When electromagnetic damping is introduced, non-synchronous vibration components, resulting from shaft asymmetries, are also eliminated. The combined theoretical and experimental studies show angular control to be a viable alternative means of reducing flexible rotor vibrations.

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This thesis considers the use of chaos concepts in investigating the dynamics of two discontinuously nonlinear mechanical systems having two degrees of freedom. The nonlinearity considered is in the form of a discontinuous stiffness effect, and can cause the systems to exhibit chaotic motion. The first system is a rotor system with a bearing clearance effect. The second is a nonlinear vibration absorber, comprising a conventional linear absorber and a linear snubber stiffness, which the auxiliary mass intermittently contacts. Numerical integration is used in solving the equations of motion for each system. Equivalent physical rigs are tested. Both the theoretical and experimental results are analysed using chaos techniques such as phase plane portraits, Poincaré maps, frequency spectra and bifurcation diagrams. Comparison made between the differently acquired results shows that fairly good correlation is obtained in both systems, for realistic values of damping. Periodic, quasiperiodic and chaotic responses are exhibited by both systems, for different combinations of system parameters, with the responses of the systems being extremely sensitive to changes in these parameters. Investigations of the rotor system concluded that quasi-periodic responses are only possible if there is some form of cross-coupling present. An effective discontinuously nonlinear absorber is developed, theoretically. A reduction in the amplitude of the second resonance peak of the linear absorber is achieved. This enables the primary system to be operated over a wider frequency range without reaching the large amplitudes to the second resonance. The non-linear absorber also has the effect of attenuating the response from the auxiliary mass. Fatigue analysis is carried out to investigate the effect of chaotic motions on mechanical components. The analysis reveals the subharmonic motions are more damaging than chaotic motions, which are in turn more damaging than simple fundamental responses.

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No description available.

This thesis examines the fundamental equations of the branch of linear oscillatory dynamics known as Statistical Energy Analysis (SEA). The investigation described is limited to the study of two, point coupled multi-modal sub-systems which form the basis for most of the accepted theory in this field. Particular attention is paid to the development of exact classical solutions against which simplified approaches can be compared. These comparisons reveal deficiencies in the usual formulations of SEA in three areas, viz., for heavy damping, strong coupling between sub-systems and for systems with non-uniform natural frequency distributions. These areas are studied using axially vibrating rod models which clarify much of the analysis without significant loss of generality. The principal example studied is based on part of the structure of a modem warship. It illustrates the simplifications inherent in the models adopted here but also reveals the improvements that can be made over traditional SEA techniques. The problem of heavy damping is partially overcome by adopting revised equations for the various loss factors used in SEA. These are shown to be valid provided that the damping remains proportional so that inter-modal coupling is not induced by the damping mechanism. Strong coupling is catered for by the use of a correction factor based on the limiting case of infinite coupling strength, for which classical solutions may be obtained. This correction factor is used in conjunction with a new, theoretically based measure of the transition between weakly and strongly coupled behaviour. Finally, to explore the effects of non-uniform natural frequency distributions, systems with geometrically periodic and near-periodic parameters are studied. This important class of structures are common in engineering design and do not posses the uniform modal statistics commonly assumed in SEA. The theory of periodic structures is used in this area to derive more sophisticated statistical models that overcome some of these limitations.

As an extension of previously reported work on effects of internal resonance on non-linear vibration of beams, it has been shown that for blade-like beams excited parametrically by support motion in the plane of maximum stiffness, complex combination instabilities are observed. In addition to the well-known sum-type combination instability existing between the fundamental out-of-plane bending and the torsional modes of the beam, investigation has revealed the occurrence of higher order instabilities producing detectable bending and torsional vibrations which are not synchronous with external excitations. These effects are subsequently shown to exist in a related way in coupled beam configurations shown to exist in a related way in coupled beam configurations under forced vibration when specific internal resonance conditions exist between the natural frequencies of the various modes, and to produce visible patterns of non-linear energy flow between modes. This study considers one such effect both experimentally and theoretically, consisting predominantly of a coupling between the fundamental and second nonplanar bending modes, and torsion mode. This combination resonance was modelled by taking the perturbation analysis to second order and including other contributory terms in the system governing equations. An expression for the transition curve for this resonance has been derived which shows the regions of stable and unstable solutions in a two parameter plane. Very close agreement is obtained between theoretical and experimental results for different beam lengths. It is also shown that if the geometry of the system is such that theses two combination resonances can be excited simultaneously, very small alternations to the internal tuning of the system can generate noticeable intermodal energy exchange effects. This system is then examined in the context of non-linear forced vibration and to this end an arrangement of coupled beams is studied. The vertical blade-like beam is coupled to the free end of a horizontal cantilever beam which is externally excited at a frequency in the region of its second bending mode frequency. This allows for the possibility of four mode interaction between the three nonplanar modes described above and also the second planar bending mode. A four-degree-of-freedom model was formulated and perturbation analysis revealed that complex multimodal responses could occur for a single-frequency excitation. Steady-state solutions were derived by means of numerical integration techniques. A reasonable degree of agreement was observed between theoretical and experimental results.

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No description available.

No description available.