A Describing Function for Dynamic Forces in Single Degree-of-Freedom Mechanisms

[+] Author and Article Information
R. R. Allen

Mechanics and Structures Department, School of Engineering and Applied Science, University of California, Los Angeles, Calif. 90024

D. M. Rozelle

J. H. Wiggins Company, Redondo Beach, Calif. 90277

J. Dyn. Sys., Meas., Control 102(4), 240-246 (Dec 01, 1980) (7 pages) doi:10.1115/1.3149609 History: Received September 01, 1980; Online July 21, 2009


In a single degree-of-freedom mechanism, a generalized force is produced by elastic, dissipative, and inertial effects. This force may be expressed as a power series in the mechanism’s generalized velocity where the coefficients are functions of the generalized displacement. Approximating the coefficients by their Fourier series expansions produces a describing function which is rapidly convergent and provides substantial computational and analytical advantages over using the exact equations. This describing function permits efficient time-domain simulation of mechanism dynamics and produces an analytical expression for the spectral content of the mechanism dynamic force. Generation and application of the describing function is illustrated by a numerical example.

Copyright © 1980 by ASME
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