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https://open.uns.ac.rs/handle/123456789/10681
Title: | The effects of strong cubic nonlinearity on the existence of periodic solutions of the Mathieu-Dufng equation | Authors: | Kovačić, Ivana Cvetićanin, Livija |
Issue Date: | 1-Dec-2009 | Journal: | Journal of Applied Mechanics, Transactions ASME | Abstract: | This paper deals with systems governed by the Mathieu-Dufng equation, with a time-dependent coefcient of the linear term and a constant, not necessarily small coefcient of the cubic term. This coefcient can be positive or negative. The method of strained parameters applied to a linear system governed by the Mathieu equation is extended to a strongly nonlinear system. As a result, the curves corresponding to the parameter values at which peri-odic solutions exist are obtained. It is shown that they strongly depend on the value of the coefcient of nonlinearity and the initial conditions. The corresponding parameter planes are plot-ted. Numerical integrations are carried out to conrm the analyti-cal results. © 2009 by ASME. | URI: | https://open.uns.ac.rs/handle/123456789/10681 | ISSN: | 218936 | DOI: | 10.1115/1.3112722 |
Appears in Collections: | FTN Publikacije/Publications |
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