Lowest critical velocity of rotating shafts.

The effect of the gyroscopic moment on the appearance of a first imaginary critical velocity (minimum negative value of lambda) is investigated and shown to have an important effect on the computation of the first critical velocity. A numerical procedure is developed which can be used for overcoming the difficulties arising when the first real and the first imaginary roots are similar in modulus. As an example, a real shaft with two supports was analyzed. For the computation the real shaft was subdivided into ten sections, and for two of them (representing compressor and turbine) the gyroscopic moment was taken into account. The present method is especially useful when high speed computational facilities are not available.