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This series of two papers focuses on the determination and clarification of the characteristics of the forced response of bladed disks that exhibit a mistuning pattern that is either harmonic or partial. Harmonic mistuning refers to single wavelength variations in structural properties along the disk while partial mistuning is associated with blade characteristics that are random in a specific sector and tuned elsewhere. The results of this analysis demonstrate that many features of the response of these simple systems match not only qualitatively but also quantitatively their counterparts on randomly mistuned bladed disks. Relying on these similarities, simple and reliable approximations of the localization factor and of the mean response are easily derived that exemplify the usefulness of harmonic and partial mistuning patterns. Finally, it is demonstrated both theoretically and by comparison with simulation results that the maximum amplitude of response of a disk closely follows a Weibull-type distribution in all coupling situations, from very weak to very strong.

This series of two papers focuses on the determination and clarification of the characteristics of the forced response of bladed disks that exhibit a mistuning pattern that is either harmonic or partial. Harmonic mistuning refers to single wavelength variations in structural properties along the disk while partial mistuning is associated with blade characteristics that are random in a specific sector and tuned elsewhere. The results of this analysis demonstrate that many features of the response of these simple systems match not only qualitatively but also quantitatively their counterparts on randomly mistuned bladed disks. Relying on these similarities, simple and reliable approximations of the localization factor and of the mean response are easily derived that exemplify the usefulness of harmonic and partial mistuning patterns. Finally, it is demonstrated both theoretically and by comparison with simulation results that the maximum amplitude of response of a disk closely follows a Weibull-type distribution in all coupling situations, from very weak to very strong.

The paper is devoted to the study of a supersonic lifting line theory intended to provide both a means of aerodynamic calculation and a benchmark for the validation of the control point position for the related constant pressure panel methods. The model is based on the small perturbations assumption. A constant distribution of bound vortices is assumed along the chord whereas the spanwise load distribution is calculated by means of trigonometrical series, formally similar to the subsonic methods. The calculated aerodynamic coefficients are in good agreement with the reference data, the precision being compatible with the small perturbations assumption. The control point position obtained is shown to vary as a function of aspect ratio from 100 to 88% of the local chord.