ISSN 0869-6632 (Print)
ISSN 2542-1905 (Online)

For citation:

Blekhman I. I., Landa P. S. Conjugate resonances in nonlinear systems under biharmonical action. Vibro-induced bifurcations. Izvestiya VUZ. Applied Nonlinear Dynamics, 2002, vol. 10, iss. 1, pp. 44-51. DOI: 10.18500/0869-6632-2002-10-1-44-51

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Language: 
Russian
Heading: 
Bifurcations in Dynamical Systems
Article type: 
Article
UDC: 
531.3+534
DOI: 
10.18500/0869-6632-2002-10-1-44-51

Conjugate resonances in nonlinear systems under biharmonical action. Vibro-induced bifurcations

Autors: 
Blekhman Ilya Israelivich, Institute of Problems of Mechanical Engineering of Russian Academy of Science
Landa Polina Solomonovna, Lomonosov Moscow State University
Abstract: 

Using a bistable oscillator described by a Duffing equation as an example, we consider resonances caused by a biharmonical external force with essentially different frequencies. We show that these resonances are conjugate; they appear when either the low or high frequency changes. The resonances take place also as the amplitude of the high-frequency action varies. Besides we show that the high-frequency action induces the bifurcation of the change in the number of stable steady states in the system; so the seeming resonance in an overdamped oscillator is caused just this bifurcation.

Key words: 
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Acknowledgments: 
This work was partially supported by the Russian Foundation for Basic Research (Grant 01-01-00227) and within the framework of the Integrated Programme 19 of the Presidium of the Russian Academy of Sciences (Project 1.4).
Reference: 
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Received: 
10.03.2002
Accepted: 
15.04.2002
Available online: 
13.12.2023
Published: 
31.07.2002
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