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Journal of Applied Nonlinear Dynamics 14(1) (2025) 189--210 | DOI:10.5890/JAND.2025.03.013

Ya.O. Lebedenko, Yu.V. Mikhlin

Department of Applied Mathematics, National Technical University ``Kharkiv Polytechnic Institute'', Kharkiv 61002, Ukraine

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Abstract

Resonant behavior of two 3-DOF systems with a limited power supply (or so-called non-ideal systems) is analyzed. Resonant steady states are constructed by the multiple scales method. Transient is presented using the two-points Pad\'{e} approximants containing exponents. Obtained analytical results are compared with a numerical simulation. It is shown that amplitudes of the resonance vibrations of the elastic sub-system can be essentially decreased by change of the system parameters.

Acknowledgments

This study is supported in part by the grant of the Ministry of Education and Science of Ukraine M2137, UDK 539.3, No. 0118U002045 and by the National Research Foundation of Ukraine, project 2023.03/0255.

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