A perturbation method is described which predicts the changes in eigenfrequencies resulting from geometrical changes of a structure. This dependence is represented by dimensionless functions, one for each eigenfrequency, which vary over the surface of the structure. The functions are presented for each eigenfrequency as isoline plots. An easily estimated integration of these functions allows one to predict a geometrical change which results in a desired change in the resonance frequencies. The method was applied to a turbine blade and a rectangular beam. For the turbine blade isoline plots are presented for the first five eigen frequencies. Eigen frequency changes up to 8 percent were modeled accurately.

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