Methods of updating numerical models in structural dynamics.

This thesis investigates several methods for updating numerical models in structural dynamics with a view to identify and develop the most suitable algorithms. To achieve this objective, the work initially focused on reviewing existing updating techniques in a broad sense. The constrained eigenstructure assignment method, often used in control applications, was identified as a possible updating route. The basic algorithm was modified so that it could deal with the updating of large-order systems and its formulation was made compatible with more conventional updating techniques such as the response function and the inverse eigensensitivity methods. Model updating based on forced vibration testing was introduced next. Its formulation and the computational aspects of the technique were described in detail. Satisfactory results were obtained, even in the case of noisy and incomplete experimental data. The effects of including damping were also addressed and some recommendations for an appropriate choice of frequency points were made. Different regularisation techniques for the solution of ill-posed problems were investigated and presented in a unified notation. Such techniques were applied to incomplete and noisy measured FRF data sets and the results obtained were considered to be superior to those computed using conventional updating methods. The use generic elements in both FE modelling and updating was considered in the later part of the work as their internal formulation allows a certain amount of solution adaptivity. The findings showed that generic elements could deal with both physical parameter errors and discretisation errors. A generic element family for rectangular plates was introduced and used successfully in the case of a uniform square 2 plate. A similar route was also followed for exact elements but the results looked less encouraging in this latter case. In parallel with updating methods, a number of fundamental questions were also addressed. The required experimental accuracy that must be attained when updating finite element models using measured vibration test data was determined via a matrix norm solution. It was shown that a well-defined relationship, that can be expressed as a characteristic function, exists between the system’s properties, the correction matrices and the actual amount of experimental noise. The formulation was then applied to the standard response function updating formulation and it was shown that the updating algorithm was dependent on a number of conditions which arose from two distinct cases: one convergent and the other divergent. Finally, the use of physical parameters in model updating is implemented and then verified by experimental case studies on two configurations of a rectangular plate. Some recommendations for further work in this area were also forwarded.