Identification of spatial models for the vibration analysis of lightly damped structures

It is accepted today that the design of structures should include consideration of their vibrational characteristics. It is thus necessary to obtain structural vibration data by measurement or by use of computer predictions and to evaluate and modify the structures so that satisfactory characteristics are ultimately achieved. The amount of data involved is difficult to handle in all but the simplest cases and so relatively simple computer models become necessary to reduce this amount and to facilitate investigation of the effects of changes of design parameters. Spatial models consist of matrices of mass, stiffness and damping properties expressed in relation to selected coordinates of interest, in particular at points of connection. The lightly damped structures featured in this thesis have the property that their natural frequencies are easily distinguished from each other. The dynamic range of their mobility properties is very large. The earlier parts of this thesis are concerned with identification of modal parameters which represent the vibration behaviour of specific points on a structure. Extension is then made to the relationship of several points which are related by natural mode shapes. It is shown that such modal data can be converted into a spatial model of the structure. Particular attention is paid to the need to measure rotational mobilities and cope with the limitations of transducers. The use of residues to represent the effects of modes beyond the range of measurement is explored. The modelling techniques are initially evaluated on error-free data for ideal systems with finite numbers of modes and beams with unlimited numbers of modes. The latter parts of the thesis are concerned with the application of the foregoing measurement and analysis techniques to physical structures. Good results are obtained for modelling a simple beam assembly and for prediction of the lowest cantilever frequency of a turbine blade based on measurements of its free-free properties.