Blade model identification and maximum amplification of forced response due to mistuning.

摘要

This research focuses on two aspects of the structural dynamic response of mistuned bladed disks; more specifically, (i) the identification of mistuning in bladed disks for the prediction of the forced response, and (ii) the estimation of the maximum forced response that can be observed on mistuned bladed disks. The availability of an accurate structural dynamic model is important when undertaking a full-scale experimental testing of a bladed disk as it permits for example the experimenter to most effectively position a small number of strain gages to capture the maximum response of the bladed disk. To address these issues; a recently introduced maximum likelihood identification procedure is considered and first validated to realistic reduced order models of bladed disks. Next, it is demonstrated that this procedure can indeed lead to a reliable prediction of the blade which will exhibit the maximum response in a forced response test. It is also found that the identification approach provides a basis to discuss mistuning quantification, i.e., to highlight how many and which structural parameters need to be considered mistuned to obtain an accurate representation of the statistical distribution of the response of mistuned bladed disks. The second part of the thesis concentrates on the estimation of the maximum amplification of the forced response of bladed disks due to mistuning. A general multi-degree-of-freedom structural dynamic model of the blades and blade sectors is adopted. An optimization effort is first undertaken in the limit of very lightly damped bladed disks that focuses on the determination of the mistuned bladed disk mode shapes the maximize a norm of the blade response. Analytic solutions of the problem are derived for some norms of practical interest and their appropriateness validated by comparison with a complete numerical optimization. It is found and justified that the mode-based optimization leads to an upper bound of the exact maximum amplification factor. Further, the derived solution is found to reduce to published results in the simple case of a single-degree-of-freedom per blade sector model. Finally, the derived form of the mode shapes is used to devise a computationally expedient approach to obtain the true maximum amplification factor of the response of mistuned bladed disks and the corresponding mistuning pattern, first in the case of a very light damping, then in the general case.