On the Stability of a Differential Equation With Application to Parametrically Excited Systems

[+] Author and Article Information
R. H. Rand, H. Simon

Department of Theoretical and Applied Mechanics, Cornell University, Ithaca, N.Y.

J. Appl. Mech 37(1), 218-220 (Mar 01, 1970) (3 pages) doi:10.1115/1.3408447 History: Received July 02, 1969; Revised October 10, 1969; Online July 12, 2010


The stability of the equation z̈ + (Δ + ε cos t)−m z = 0, where m is a positive integer, is studied by using Floquet theory and perturbations. The results are confirmed by a digital computer program based on Floquet theory. Physical examples involving parametric excitation for m = 1, 3 are cited from the literature.

Copyright © 1970 by ASME
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