Asymptotic Theory of a Slender Rotating Beam With End Masses

[+] Author and Article Information
A. M. Whitman, J. M. Abel

Towne School of Civil and Mechanical Engineering, University of Pennsylvania, Philadelphia, Pa.

J. Appl. Mech 39(2), 569-576 (Jun 01, 1972) (8 pages) doi:10.1115/1.3422719 History: Received May 18, 1970; Revised February 15, 1971; Online July 12, 2010


The method of matched asymptotic expansions is employed to solve the singular perturbation problem of the vibrations of a rotating beam of small flexural rigidity with concentrated end masses. The problem is complicated by the appearance of the eigenvalue in the boundary conditions. Eigenfunctions and eigenvalues are developed as power series in the perturbation parameter β1/2 and results are given for mode shapes and eigenvalues through terms of the order of β.

Copyright © 1972 by ASME
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