TY - GEN
T1 - Consistent modeling of rotating timoshenko shafts subject to axial loads
AU - Choi, S. H.
AU - Pierre, C.
AU - Ulsoy, A. G.
N1 - Publisher Copyright:
© 1991 Proceedings of the ASME Design Engineering Technical Conference
PY - 1991
Y1 - 1991
N2 - 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.
AB - 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.
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U2 - 10.1115/DETC1991-0234
DO - 10.1115/DETC1991-0234
M3 - Conference contribution
AN - SCOPUS:85104774081
T3 - Proceedings of the ASME Design Engineering Technical Conference
SP - 93
EP - 104
BT - 13th Biennial Conference on Mechanical Vibration and Noise
T2 - ASME 1991 Design Technical Conferences, DETC 1991
Y2 - 22 September 1991 through 25 September 1991
ER -