Measurement of the Multivalued Phase Curves of a Strongly Nonlinear System by Fixed Frequency Tests

G Zhang, C Zang (Nanjing University of Aeronautics and Astronautics, China) & MI Friswell (Swansea University)

Archive of Applied Mechanics, Vol. 90, No. 11, November 2020, pp. 2543-2560


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 drop-out 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.

Paper Availability

This material has been published in the Archive of Applied Mechanics, Vol. 90, No. 11, November 2020, pp. 2543-2560. Copyright and all rights therein are retained by Springer.

Link to paper using doi: 10.1007/s00419-020-01736-w

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