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Stability of similar nonlinear normal modes under random excitation

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Abstract

Two-DOF nonlinear system under stochastic excitation is considered. It is assumed that the system allows from two up to four nonlinear normal modes (NNMs) with rectilinear trajectories in the system configuration space. Influence of the random excitation to the NNMs stability is analyzed by using the analytical–numerical test, which is an implication of the well-known stability definition by Lyapunov. Boundary of the stability/instability regions is obtained in plane of the system parameters. Stability of the NNMs under deterministic chaos excitation is also considered.

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Acknowledgements

This study was supported in part by the Ministry of Education and Science of Ukraine (research Project DR 0118U002045).

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  1. Department of Applied Mathematics, National Technical University “KhPI“, Kharkiv, Ukraine

    Y. V. Mikhlin & G. V. Rudnyeva

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  1. Y. V. Mikhlin
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  2. G. V. Rudnyeva
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Correspondence to G. V. Rudnyeva.

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Mikhlin, Y.V., Rudnyeva, G.V. Stability of similar nonlinear normal modes under random excitation. Nonlinear Dyn 103, 3407–3415 (2021). https://doi.org/10.1007/s11071-020-06093-5

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