Amplitude Modulation of a Forced System by Parameter Variation

[+] Author and Article Information
K. Eisinger

Marine Systems, The Boeing Company, P. O. Box 3707, MS 61-35, Seattle, Wash. 98124

H. C. Merchant

Department of Mechanical Engineering, 204 MEB, FU-10, University of Washington, Seattle, Wash. 98195

J. Appl. Mech 46(1), 191-196 (Mar 01, 1979) (6 pages) doi:10.1115/1.3424495 History: Received February 01, 1978; Revised August 01, 1978; Online July 12, 2010


Classical (primary) parametric amplification is reviewed. This phenomenon is known to occur for a parametric variation with a frequency of twice that of a harmonic input in the neighborhood of a system’s characteristic frequency. A higher-order phenomenon that is identified as secondary parametric amplification (or attenuation), is discussed in detail and solutions related to Mathieu’s equation are presented. Its occurrence is characterized by a frequency of the parametric variation that is of the order of 2α/n (where n = 1, 2, 3, [[ellipsis]], and α is the undamped characteristic frequency of the system) and a harmonic input of a much lower frequency. The amplification (or attenuation) resulting from the secondary parametric amplification phenomenon is manifested in an overmodulated response that must be low-pass filtered to recover the desired low frequency response.

Copyright © 1979 by ASME
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