The Transverse Vibration of a Doubly Tapered Beam

[+] Author and Article Information
D. O. Banks, G. J. Kurowski

Department of Mathematics, University of California, Davis, Calif.

J. Appl. Mech 44(1), 123-126 (Mar 01, 1977) (4 pages) doi:10.1115/1.3423976 History: Received July 01, 1976; Online July 12, 2010


We analyze the transverse vibrations of a thin homogeneous beam which is symmetric with respect to the x-y and x-z planes. The cross section of the beam at x is assumed to have the form

D(x) = {(x, y, z)|x ∊ [0, 1],
  y = xαy1,
  z = xβz1,
  (y1, z1) ∊ D1}
where D1 is the cross section at x = 1. Expressions are obtained from which the eigenvalues and eigenfunctions can be easily found for 0 ≤ α < 2 and all combinations of clamped, hinged, guided, and free boundary conditions at both ends of the beam.

Copyright © 1977 by ASME
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