On the Nonlinear Vibrations of Free-Free Beams

[+] Author and Article Information
Kuo-Kuang Hu, Philip G. Kirmser

Department of Applied Mechanics, Kansas State University, Manhattan, Kans.

J. Appl. Mech 38(2), 461-466 (Jun 01, 1971) (6 pages) doi:10.1115/1.3408798 History: Received January 19, 1970; Revised May 04, 1970; Online July 12, 2010


A nonlinear partial differential equation which describes the natural free-free vibrations of beamlike structures is derived, and then solved approximately by reduction to a nonlinear ordinary differential equation through the use of the Duffing and Ritz-Kantorovich methods. This ordinary differential equation, which is a nonlinear eigenvalue problem, is then solved by perturbation and shooting methods. The solutions show that higher modes of vibration are not possible for the nonlinear vibration.

Copyright © 1971 by ASME
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