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TITLE: Vibration of a rotating shaft by the "Timoshenko beam" Theory AUTHORS: Porat, I. (1934-2012), Niv, M. SOURCE: Israel J. Technol., v. 9, No. 5, pp. 535-546 (1971).
LANGUAGE: English. 8 references. ABSTRACT SOURCE: Israel J. Technol., v. 9, No. 5, p. 535 (1971).
ABSTRACT:
The equation of motion of a rotating symmetrical shaft was solved under the basic
assumption of the "Timoshenko beam theory" (allowance for shear and rotary inertia)
and gyroscopic moments. The relation between rotational speed and natural vibration
frequency is given for every mode, and the forward and backward resonance equation is
derived from it. A physical interpretation is given, based on familiar dynamic effects,
and it is proved that only forward resonance is caused by the rotation! There are
four natural vibration frequencies (two positive and two negative) for every mode, one
pair with "low" frequency values, (Euler's solution) and the other with high ones. At
high speeds, the high-level natural frequencies are identical for all modes. This is
explained by a mechanical model.
● COMMENT: Proceedings of the Nineteenth Israel Annual Conference on Theoretical and Applied Mechanics, Haifa, September 5, 1971.
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