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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