Nonlinear Vibrations of a Beam Under Harmonic Excitation

[+] Author and Article Information
W. Y. Tseng, J. Dugundji

Department of Aeronautics and Astronautics, Massachusetts Institute of Technology, Cambridge, Mass.

J. Appl. Mech 37(2), 292-297 (Jun 01, 1970) (6 pages) doi:10.1115/1.3408504 History: Received February 18, 1969; Revised August 15, 1969; Online April 06, 2010


A straight beam with fixed ends, excited by the periodic motion of its supporting base in a direction normal to the beam span, was investigated analytically and experimentally. By using Galerkin’s method (one mode approximation) the governing partial differential equation reduces to the well-known Duffing equation. The harmonic balance method is applied to solve the Duffing equation. Besides the solution of simple harmonic motion (SHM), many other branch solutions, involving superharmonic motion (SPHM) and subharmonic motion (SBHM), are found experimentally and analytically. The stability problem is analyzed by solving a corresponding variational Hill-type equation. The results of the present analysis agree well with the experiments.

Copyright © 1970 by ASME
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