An Application of Diakoptics in the Determination of Turbine Bucket Frequencies by the Use of Perturbations

The method of Diakoptics, originally designed for the computation of linear electrical network, is also applicable to those linear systems of mechanics, where major subsystems are not too strongly coupled with one another. The method deals with the subsystems individually in a first step and takes care of the effects of weak coupling in a second one. If the systems are represented by a set of simultaneous algebraic equations, the procedure of Diakoptics manifests itself in various additive and multiplicative matrix decompositions. Diakoptics in combination with a method of perturbation is applied to determine the natural frequencies of a group of buckets coupled by tie-wires and/or a cover. Starting with the natural frequency and corresponding mode shape of the single bucket we obtain the frequency of the coupled system by a method of perturbation. An algorithm is derived in order to compute perturbation coefficients as they appear in a series expansion of a certain matrix. It is found that the proper representation of the single bucket is of utmost importance in obtaining accurate coupling frequencies. The results for the coupling frequencies of various groups of buckets calculated using this procedure correlate well with test results. Different mode shape combinations and the coupling effect of the cover, and cover and tie-wire combination are also considered. Comparison of our results with those obtained by the Prohl-Myklestad method as well as with experiments indicates that both methods are compatible with one another. It appears, however, that the method of Diakoptics in combination with a perturbation on the Prohl-Myklestad method requires much less numerical work.