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UNSTABLE VIBRATIONS AND BUCKLING OF ROTATING FLEXIBLE RODS
W. D. LAKIN and A. NACHMAN
Quarterly of Applied Mathematics
Vol. 35, No. 4 (JANUARY 1978), pp. 479-493
Published by: Brown University
Stable URL: http://www.jstor.org/stable/43636890
Page Count: 15
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We consider a group of fourth-order boundary-value problems associated with the small vibrations or buckling of a uniform flexible rod which is clamped at one end and rotates in a plane perpendicular to the axis of rotation. The vibrations may be in any plane relative to the plane of rotation and the rod is off-clamped, i.e. the axis of rotation does not pass through the rod's clamped end. The governing equation for the vibrations involves a small parameter for rapid rotation and must be treated by singular perturbation methods. Further, a turning point of the equation always coincides with a boundary point. Both free and unstable vibrations are examined, and a stability boundary is obtained. Results for the unstable vibrations predict the unexpected existence of a time-independent buckled state in non-transverse planes when the rod is wholly under tension. The general buckling problem in the transverse plane is also considered.
Quarterly of Applied Mathematics © 1978 Brown University