Measurement of the multivalued phase curves of a strongly nonlinear system by fixed frequency tests
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O R I G I NA L
Genbei Zhang · Chaoping Zang
· Michael I. Friswell
Measurement of the multivalued phase curves of a strongly nonlinear system by fixed frequency tests
Received: 25 December 2019 / Accepted: 7 July 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
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. Keywords Fixed frequency test · Strongly nonlinear system · Multivalued phase curve · Force dropout · Phase shift
1 Introduction A strongly nonlinear system can have multiple solutions, and this is a clear difference between linear and nonlinear oscillations [1]. The multivalued response is responsible for jump phenomena [2]. The theoretical study of the multivalued response of strongly nonlinear systems has been discussed in detail [2]. Given the vast literature on the analytical and experimental response of nonlinear structures, only the most relevant are selected in this overview. However, measurement of the multivalued response of a strongly nonlinear system is challenging. Zhang et al. [3] have summarized the different measurement methods, including the controlled-level vibration test method (CLV) [4], the intelligent nonlinear coupling analysis method (INCA) [5,6], the control-based continuation method (CBC) [7–12], and the synthesis of nonlinear frequency responses (SNFS) [13]. The CLV method G. Zhang · C. Zang (B) Jiangsu Province Key Laboratory of Aerospace Power System, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, People’s Republic of China E-mail: [email protected] M. I. Friswell College of Engineering, Swansea Unive
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