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Measurement of the multivalued phase curves of a strongly nonlinear system by fixed frequency tests

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Abstract

The steady-state response of a strongly nonlinear system often has multiple solutions under harmonic excitation, which includes both multiple response amplitudes and multiple phases. Taking advantage of the force dropout phenomenon of electrodynamic shakers near resonance, a fixed frequency test method was proposed previously to measure the multivalued amplitude curves continuously. This method is further developed in this paper to measure the multivalued phase curves, which represent the degree by which the response lags the excitation, synchronously and continuously using the input voltage as the continuation parameter. The multivalued phase curve of a strongly nonlinear system is found to contain abundant information and is closely related to the multivalued amplitude curve. The phases of the response and excitation of a strongly nonlinear system are extracted accurately by the period resampling technique usually used in rotor dynamics tests. The phase shift of the electrodynamic shaker is large when the force drops out near resonance in fixed frequency tests. This phenomenon is used to measure the multivalued phase curves, together with the multivalued amplitude curves. An experimental test of a strongly nonlinear single degree of freedom system is used to demonstrate this method. The evolution of the phase curves and the corresponding relationship with the amplitude curves in fixed frequency tests are discussed. Numerical simulation is also undertaken to validate this method.

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Acknowledgements

The authors gratefully appreciate the financial support for this work provided by the National Natural Science Foundation of China and National Safety Academic Foundation of China (No. U1730129), The Cultivation Foundation of National Defense Large Projects of China (No. NP2018450), Jiangsu Innovation Program for Graduate Education (Project No. CXLX13_167), the Fundamental Research Funds for the Central Universities, Funding for Outstanding Doctoral Dissertation in NUAA (Project No. BCXJ13-04). The support of the Jiangsu Province Key Laboratory of Aerospace Power System, the Key Laboratory of Aero-engine Thermal Environment and Structure, Ministry of Industry and Information Technology are also gratefully acknowledged.

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Authors and Affiliations

  1. Jiangsu Province Key Laboratory of Aerospace Power System, Nanjing University of Aeronautics and Astronautics, Nanjing, 210016, People’s Republic of China

    Genbei Zhang & Chaoping Zang

  2. College of Engineering, Swansea University, Swansea, SA1 8EN, UK

    Michael I. Friswell

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  1. Genbei Zhang
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  2. Chaoping Zang
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  3. Michael I. Friswell
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Correspondence to Chaoping Zang.

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Zhang, G., Zang, C. & Friswell, M.I. Measurement of the multivalued phase curves of a strongly nonlinear system by fixed frequency tests . Arch Appl Mech 90, 2543–2560 (2020). https://doi.org/10.1007/s00419-020-01736-w

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