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The instantaneous phase difference between two parametric-excited cables with distinct parameters: characteristics and origination

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Abstract

The phase-frequency characteristic is a fundamental feature of cables closely related to the synchronization phenomena. The response phase of a nonlinear vibrating cable under a specific excitation frequency is commonly believed to be the constant value in the linear solution, while higher-order terms (HOTs) are commonly omitted. However, as the variation of cable parameters, the HOTs would significantly contribute to the response and thus change the phase instantaneously. In order to ascertain the instantaneous phase difference between cables with the consideration of the HOTs, the instantaneous phase-frequency characteristics of two parametric-excited nonidentical suspended cables are investigated. The dimensionless dynamic equations of a two-cable system were derived, and the discrete model was obtained using the Galerkin method and then solved by the Multiple Scales Method (MSM). The MSM solution was verified simultaneously using the Runge–Kutta method (R-K) and the Finite Element Method (FEM). Results show that the HOTs’ influence on the instantaneous phase is non-negligible in some frequency ranges. The origination of the instantaneous phase difference between the two distinct cables comes from two aspects: (i) the difference in phase shift values (PSVs) of linear terms; and (ii) the proportion difference of drift terms (DTs) in HOTs.

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The current study’s data are available from the corresponding author upon reasonable request.

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Acknowledgements

Thanks to Cong Li for his help in the verification and comparison of the revised manuscript.

Funding

This work was supported by the National Natural Science Foundation of China (grant number 51808085).

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Authors and Affiliations

  1. College of Civil Engineering, Chongqing Jiaotong University, 66 Xuefu Avenue, Nan’an District, Chongqing, Chongqing, 400074, China

    Ceshi Sun, Junqiang Lin & Dewang Jiao

  2. Department of Design, Hu’nan City University Design and Research Institute Co., Ltd, No. 18, Jianshan Road, Changsha High-tech Development Zone, Changsha, 410005, Hu’nan, China

    Zhengke Deng

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  1. Ceshi Sun
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Correspondence to Ceshi Sun.

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Sun, C., Lin, J., Deng, Z. et al. The instantaneous phase difference between two parametric-excited cables with distinct parameters: characteristics and origination. Nonlinear Dyn 111, 9939–9955 (2023). https://doi.org/10.1007/s11071-023-08344-7

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