Forced Lateral Vibration of a Uniform Cantilever Beam With Internal and External Damping

[+] Author and Article Information
Ho Chong Lee

Department of Mechanical Engineering, Rensselaer Polytechnic Institute, Troy, N. Y.

J. Appl. Mech 27(3), 551-556 (Sep 01, 1960) (6 pages) doi:10.1115/1.3644039 History: Received May 28, 1959; Online September 16, 2011


The steady-state response problem of a uniform beam with a sinusoidal shaking force at the base is studied for the case where the beam material is the general linear substance represented by a model having an additional spring element in parallel with the Maxwell elements. In the analysis, the stress-strain relationship is applied only to the longitudinal strain of the beam, leaving the shear stress-strain relation to be that of a perfectly elastic material. The exact solution with a numerical example is given for one case where the shear and rotatory inertia effects are neglected. This result is compared with the solution obtained by a tabular method. The results of both methods are in excellent agreement.

Copyright © 1960 by ASME
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