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

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 ter...

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Bibliographic Details
Published in:Nonlinear dynamics 2023-06, Vol.111 (11), p.9939-9955
Main Authors: Sun, Ceshi, Lin, Junqiang, Deng, Zhengke, Jiao, Dewang
Format: Article
Language:English
Subjects:
Automotive Engineering
Cables
Classical Mechanics
Control
Dynamical Systems
Engineering
Finite element method
Frequency ranges
Galerkin method
Mechanical Engineering
Original Paper
Parameters
Phase shift
Runge-Kutta method
Synchronism
Vibration
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Summary: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.
ISSN:0924-090X
1573-269X
DOI:10.1007/s11071-023-08344-7