You are not currently logged in.
Access your personal account or get JSTOR access through your library or other institution:
If You Use a Screen ReaderThis content is available through Read Online (Free) program, which relies on page scans. Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
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
Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Preview not available
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