Abstract
In a number of mechanical problems, systems of differential equations with periodic coefficients have to be considered, which, in general, possess not only linear but also nonlinear terms. In this paper, the first order instability region of the Mathieu equation is examined when additional nonlinear terms are present. These terms can be of the damping or restoring type.
A case of combination resonance, in the presence of nonlinear terms, is discussed for a system with two degrees of freedom. The influence of the nonlinear terms on the instability region of the first order and of first type is considered. In both problems Bogoliubov and Mitropolsky’s asymptotic method is used.
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© 1970 D. Reidel Publishing Company, Dordrecht-Holland
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Hagedorn, P. (1970). Parametric Resonance in Certain Nonlinear Systems. In: Giacaglia, G.E.O. (eds) Periodic Orbits, Stability and Resonances. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-3323-7_41
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DOI: https://doi.org/10.1007/978-94-010-3323-7_41
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-3325-1
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