Nonlinear Vibration of Beams Using a Form-Function Approximation

[+] Author and Article Information
C. L. Lou

Ford Motor Company, Dearborn, Mich.

D. L. Sikarskie

Department of Aerospace Engineering, The University of Michigan, Ann Arbor, Mich.

J. Appl. Mech 42(1), 209-214 (Mar 01, 1975) (6 pages) doi:10.1115/1.3423520 History: Received March 01, 1974; Revised June 01, 1974; Online July 12, 2010


The nonlinear response and stability of a vibrating, buckled beam is analyzed using a form-function approximation. Such an approximation differs from the usual linear series approximations in that the unknown parameter appears nonlinearly. This new approximation has two major advantages. Since all harmonics (in both space and time) are represented, the dominant harmonics are “singled out” in the solution, thus making it very efficient. The form-function representation also permits an insight into system behavior not found in other methods. Knowledge of the form parameter shows explicitly how the form of the response changes with the system parameters, e.g., forcing function magnitude and frequency, material constants, etc.

Copyright © 1975 by ASME
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