Transverse Vibrations of Cantilever Beams Having Unequal Breadth and Depth Tapers

[+] Author and Article Information
B. Downs

Department of Mechanical Engineering, Loughborough University of Technology, Loughborough, Leicestershire, LE11 3TU, England

J. Appl. Mech 44(4), 737-742 (Dec 01, 1977) (6 pages) doi:10.1115/1.3424165 History: Received October 01, 1976; Revised March 01, 1977; Online July 12, 2010


Natural frequencies of doubly symmetric cross section, isotropic cantilever beams, based on both Euler and Timoshenko theories, are presented for 36 combinations of linear depth and breadth taper. Results obtained by a new dynamic discretization technique include the first eight frequencies for all geometries and the stress distribution patterns for the first four (six) modes in the case of the wedge. Comparisons are drawn wherever possible with exact solutions and with other numerical results appearing in the literature. The results display outstanding accuracy and demonstrate that it is possible to model with high precision the dynamic behaviour of continuous systems by discretization on to a strictly limited number of degrees of freedom.

Copyright © 1977 by ASME
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