The Effects of Strong Cubic Nonlinearity on the Existence of Periodic Solutions of the Mathieu-Duffing Equation

Ivana Kovacic; Livija Cveticanin

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The Effects of Strong Cubic Nonlinearity on the Existence of Periodic Solutions of the Mathieu-Duffing Equation

机译：The Effects of Strong Cubic Nonlinearity on the Existence of Periodic Solutions of the Mathieu-Duffing Equation

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摘要

This paper deals with systems governed by the Mathieu-Duffing equation, with a time-dependent coefficient of the linear term and a constant, not necessarily small coefficient of the cubic term. This coefficient 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 periodic solutions exist are obtained. It is shown that they strongly depend on the value of the coefficient of nonlinearity and the initial conditions. The corresponding parameter planes are plotted. Numerical integrations are carried out to confirm the analytical results.

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来源
《Journal of Applied Mechanics》 |2009年第5期|054501-1-054501-3|共3页
作者
Ivana Kovacic; Livija Cveticanin;
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作者单位

Department of Mechanics, Faculty of Technical Sciences, University of Novi Sad;

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正文语种英语
中图分类应用力学;
关键词
Mathieu-Duffing equation; Strong nonlinearity; Periodic solution;

The Effects of Strong Cubic Nonlinearity on the Existence of Periodic Solutions of the Mathieu-Duffing Equation

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