Chaotic Amplitude Dynamics for Parametrically Excited Systems With Quadratic Nonlinearities
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Abstract Dynamical systems with two degrees-of-freedom, with quadratic nonlinearities and parametric excitations are studied in this analysis. The 1:2 superharmonic internal resonance case is analyzed. The method of harmonic balance is used to obtain a set of four first-order amplitude equations that govern the dynamics of the first-order approximation of the response. An analytical technique, based on Melnikov’s method is used to predict the parameter range for which chaotic dynamics exist in the undamped averaged system. Numerical studies show that chaotic responses are quite common in these quadratic systems and chaotic responses occur even in presence of damping.
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1999 ◽
Vol 08
(05)
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pp. 461-483
2014 ◽
Vol 20
(1)
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pp. 132-141
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1998 ◽
Vol 12
(1)
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pp. 11-17
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1992 ◽
Vol 47
(3)
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pp. 683-694
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2017 ◽
Vol 110
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pp. 349-359
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