The present method is an adaptation of the well-known process devised by Holzer for solving the differential equations of beam vibrations. Several versions of this method are now in common use; the original form is described in references 1 and 2 and is usually employed in computing the torsional modes of vibration of a bar carrying a series of concentrated discs. Similar processes were devised by Myklestad and Bellin for bending modes, and recently an extension of the above principle to the computation of coupled modes has been published. All of the above methods have in common the feature that a value of the frequency is assumed and a deflection computed which satisfies all but one of the required end conditions. Although the same principle forms the basis for the following method, the system of numerical integration employed makes the method better suited to configurations with continuous mass and stiffness distributions. The process is set up in such a manner as to be easily adapted to routine calculation by a semiskilled computer and the correctness of the results may be verified at each station. All of the features that make the Holzer method practical are retained, and some new techniques not in common practice are introduced.
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Henry E. Fettis (1949) studied this question.