Modes and Frequencies of Transversely Isotropic Slightly Curved Timoshenko Beams

[+] Author and Article Information
J. N. Rossettos, D. C. Squires

Department of Mechanical Engineering, Northeastern University, Boston, Mass.

J. Appl. Mech 40(4), 1029-1034 (Dec 01, 1973) (6 pages) doi:10.1115/1.3423120 History: Received May 01, 1972; Revised December 01, 1972; Online July 12, 2010


An analysis of the vibration of transversely isotropic Timoshenko beams, which have small constant initial curvature, is presented, and a closed-form general solution to the governing equations is derived. Natural modes and frequencies are determined for both clamped and simply supported end conditions, and comparisons are made. The combined effects of initial curvature, transverse shear deformation, and boundary conditions are evaluated and discussed. Specifically, it is shown in what manner the clamped beam tends to be more sensitive to shear deformation than the simply supported beam, and how initial curvature reduces the difference. Calculations also show how, in cases where shear deformation becomes more important, the initial curvature has a correspondingly smaller influence on the results.

Copyright © 1973 by ASME
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