Consistent modeling of rotating timoshenko shafts subject to axial loads

S. H. Choi, C. Pierre, A. G. Ulsoy

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

The equations of motion of a flexible rotating shaft have been typically derived by introducing gyroscopic moments, in an inconsistent manner, as generalized work terms in a Lagrangian formulation or as external moments in a Newtonian approach. This paper presents the consistent derivation of a set of governing differential equations describing the flexural vibration in two orthogonal planes and the torsional vibration of a straight rotating shaft with dissimilar lateral principal moments of inertia and subject to a constant compressive axial load. The coupling between flexural and torsional vibration due to mass eccentricity is not considered. In addition, a new approach for calculating correctly the effect of an axial load for a Timoshenko beam is presented based on the change in length of the centroidal line. It is found that the use of either a floating frame approach with the small strain assumption or a finite strain beam theory is necessary to obtain a consistent derivation of the terms corresponding to gyroscopic moments in the equations of motion. However, the virtual work of an axial load through the geometric shortening appears consistently in the formulation only when using a finite strain beam theory.

Original languageEnglish
Title of host publication13th Biennial Conference on Mechanical Vibration and Noise
Subtitle of host publicationRotating Machinery and Vehicle Dynamics
Pages93-104
Number of pages12
ISBN (Electronic)9780791806265
DOIs
StatePublished - 1991
EventASME 1991 Design Technical Conferences, DETC 1991 - Miami, United States
Duration: 22 Sep 199125 Sep 1991

Publication series

NameProceedings of the ASME Design Engineering Technical Conference
VolumePart F168436-2

Conference

ConferenceASME 1991 Design Technical Conferences, DETC 1991
Country/TerritoryUnited States
CityMiami
Period22/09/9125/09/91

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