Abstract A method for the separation of close modes by the sequential application of fictitious modifications is applied to cyclically symmetric and axisymmetric structures. The theoretical approach, based on the manipulation of measured receptances from linear systems, is applied to two physical problems; a slotted retaining nut and the turbine casing from an aero-engine. Synthesised receptances from a multiple-input multiple-output curve-fitting routine are used in order to reduce the effect of measurement noise. However, it is revealed that certain of the receptances obtained by adding a fictitious mass (or grounded spring) are very sensitive to measurement inaccuracies at the natural frequencies of the unmodified structure. Fortunately, not all of the modified receptances are sensitive in this way, and the insensitive ones are sufficient to allow an accurate estimation of the natural frequencies and mode shapes of a system modified by a point mass.
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