Abstract
In 1945, Morris† gave an analytical method for the determination of coupled engine torsional and propeller flexural vibrations, in which account was taken of blade section, blade twist, hub moment of inertia, pitch-setting angle, and speed of rotation. A particular case involved mathematically the determination of the latent roots and their associated modes for a symmetrical square matrix of the twelfth order, and in 1942 the necessary calculation took about three months. Here it is shown that, given the latent roots and their associated modes for one such case, the corresponding latent roots and modes for a similar case (in which the ‘deflexion coefficients’ are changed by arbitrary but small amounts) can be deduced explicitly, so that the additional calculation for each case after the first requires only a day or two. Extension to the case where the changes are not small is tentatively considered.
The results here given are derived by the ‘Escalator’ method; they could be applied to a wide range of problems concerning oscillations and vibrations.
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