The effects of strong cubic nonlinearity on the existence of periodic solutions of the mathieu–duffing equation
The effects of strong cubic nonlinearity on the existence of periodic solutions of the mathieu–duffing equation
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
1-3
Kovacic, Ivana
a84bc948-5aa9-444f-8a58-12a731808a20
Cvetcanin, Livija
118109de-a322-4c21-bff9-216b258590b4
September 2009
Kovacic, Ivana
a84bc948-5aa9-444f-8a58-12a731808a20
Cvetcanin, Livija
118109de-a322-4c21-bff9-216b258590b4
Kovacic, Ivana and Cvetcanin, Livija
(2009)
The effects of strong cubic nonlinearity on the existence of periodic solutions of the mathieu–duffing equation.
Journal of Applied Mechanics, 76 (5 (054501)), .
(doi:10.1115/1.3112722).
Abstract
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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Published date: September 2009
Organisations:
Dynamics Group
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Local EPrints ID: 79130
URI: http://eprints.soton.ac.uk/id/eprint/79130
ISSN: 0021-8936
PURE UUID: 247af40c-641d-4507-b34e-0746f3f97882
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Date deposited: 15 Mar 2010
Last modified: 14 Mar 2024 00:28
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Author:
Ivana Kovacic
Author:
Livija Cvetcanin
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