Planar Nonlinear Galloping of Iced Transmission Lines under Forced Self-Excitation Conditions

Liu, Xiaohui; Wu, Chuan; Zou, Ming; Min, Guangyun; Sun, Ceshi; Cai, Mengqi

doi:10.1155/2021/6686028

Cited by 7 publications

(15 citation statements)

References 29 publications

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“…(21). As the excitation amplitude p=0.5 increases to p=5, the response amplitude of self-excited vibration decreases from the point ab to the point ac; when the excitation amplitude p=8.0, the response amplitude of self-excited vibration tends to be close to 0, which also verifies the correctness of discriminant formula (20) and (21).…”

Section: A T T a T T I T T B P Wsupporting

confidence: 65%

“…When the excitation amplitude p=8, the forced-self-excited system satisfies discriminant formula (21), and the vibration form is the forced vibration regulated by Rayleigh damping. (21).…”

Section: A T T a T T I T T B P Wmentioning

confidence: 99%

“…When the excitation amplitude p=8, the forced-self-excited system satisfies discriminant formula (21), and the vibration form is the forced vibration regulated by Rayleigh damping. (21). As the excitation amplitude p=0.5 increases to p=5, the response amplitude of self-excited vibration decreases from the point ab to the point ac; when the excitation amplitude p=8.0, the response amplitude of self-excited vibration tends to be close to 0, which also verifies the correctness of discriminant formula (20) and (21).…”

Section: A T T a T T I T T B P Wmentioning

confidence: 99%

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Forced-self-excited System of Iced Transmission Lines under Planar Harmonic Excitations

Liu

Min

Sun

et al. 2021

Preprint

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This paper is concerned with the analysis of the self-excited vibrations and forced vibrations of the iced transmission lines. By introducing the external excitation load, the effect of dynamic wind on the nonlinear vibration equations of motion is reflected by vertical aerodynamic force. The approximate analytical solution of the non-resonance, and the amplitude frequency response relation of the principal resonance of the forced self-excited system are obtained by using the multiple scale method. With the increase in excitation amplitude, the nonlinearity of the system is enhanced, and the forced-self-excited system experiences three vibration stages (self-excited vibration, the superposition form of self-excited vibration and forced vibration, forced vibration controlled by nonlinear damping). Among them, the accuracy of the approximate analytical solution decreases with the increase of the nonlinear strength. And the excitation amplitude is greater than the critical value, the quenching phenomenon appear in the forced-self-excited system, and the discriminant formula is derived in this paper. In addition, the frequency of excitation term determines the vibration form of the system. The principal resonance, super-harmonic resonance and sub-harmonic resonance of the forced-self-excited system are analyzed by using different excitation frequencies. Compared with the principal resonance and the harmonic resonance, the meaningful transition from periodic response to quasi periodic response is easy to appear with the condition of the 1/3-order sub-harmonic and the 3-order super-harmonic. The conclusions would be helpful to the practical engineering of the iced transmission lines. More important, as a combination of Duffing equation and Rayleigh equation, the forced-self-excited system also has high theoretical research value.

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Section: A T T a T T I T T B P Wsupporting

confidence: 65%

“…When the excitation amplitude p=8, the forced-self-excited system satisfies discriminant formula (21), and the vibration form is the forced vibration regulated by Rayleigh damping. (21).…”

Section: A T T a T T I T T B P Wmentioning

confidence: 99%

Section: A T T a T T I T T B P Wmentioning

confidence: 99%

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Forced-self-excited System of Iced Transmission Lines under Planar Harmonic Excitations

Liu

Min

Sun

et al. 2021

Preprint

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“…e model of the current-carrying conductors is established as shown in Figure 1. e model is exposed to the unsteady wind U as a whole, uniformly acting all along their spans, where AB and CD are two long direct parallel currentcarrying conductors spaced 2b, and the current-carrying intensity is I; the middle one is a tension current-carrying conductor hinged at both ends, with the lengths of the span is L and a current-carrying intensity of i, which is subjected to external harmonic excitation Fcos(Ωt) (the external excitation caused by the unsteady part of the natural wind can be simplified to this load [27][28][29] where F is the excitation amplitude and Ω is the excitation frequency). In order to obtain the nonlinear vibration equation of the conductor, the Cartesian coordinate system O-x-y-z is established with the left suspension point of the middle tension currentcarrying conductor as the origin.…”

Section: Nonlinear Vibration Equationmentioning

confidence: 99%

“…ey stated that the steady component of the wind is responsible for self-excitation, while the turbulent part causes both parametric and external excitation in a specific resonance condition. On this basis, Liu X et al [29] considered adding the external excitation load into the governing equation of iced transmission lines under the condition of stable wind and established a new forced selfexcitation system to study the influence of dynamic wind on the nonlinear galloping characteristics of iced transmission lines.…”

Section: Introductionmentioning

confidence: 99%

Investigation on the Nonlinear Vibration Characteristics of Current-Carrying Crescent Iced Conductors under Aerodynamic Forces, Ampere’s Forces, and Forced Excitation Conditions

Liu

Haobo

Min³

et al. 2021

Discrete Dynamics in Nature and Society

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Aiming at the problem of nonlinear vibration of current-carrying iced conductors, the aerodynamic forces are introduced into the previous vibration equation of current-carrying conductors that only considered Ampere’s forces. At the same time, on this basis, a forced excitation load is further introduced to study the influence of dynamic wind on the nonlinear vibration characteristics of current-carrying iced conductors, and a new current-carrying iced conductors system under the combined action of Ampere’s forces, forced excitation, and aerodynamic forces has been established, and the improved theoretical modeling of current-carrying iced transmission lines made the model more in line with practical engineering. Firstly, the model of current-carrying iced conductors was established, and then the vibration equation of the model was derived. And the vibration equation was transformed into a finite dimensional ordinary differential equation by using the Galerkin method. The amplitude-frequency response functions of the nonlinear forced primary resonances and super-harmonic and subharmonic resonances of the system are derived by using the multiscale method. Through numerical calculation, the influence of current-carrying, spacing, wind velocity, tension, and excitation amplitude on the response amplitude when the primary resonance of the system appears is analyzed, and the difference between the two working conditions (considering the aerodynamic forces and without considering aerodynamic forces) is compared. The influence of the variation of current-carrying i on the response amplitude of super-harmonic and subharmonic resonances and the stability of the steady-state solution of forced primary resonance was analyzed. The results show that the response amplitude and the nonlinearilty of system under the action of aerodynamic forces are smaller and weaker than without the action of aerodynamic forces; the variation of line parameters has a certain influence on the response amplitude of conductor and the nonlinearity of system; the response amplitudes of the primary resonance, super-harmonic resonance, and subharmonic resonance increase with the increase in the excitation amplitudes, and the resonance peak is offset towards the negative value of the tuning parameter σ, showing the characteristics of soft spring, and the response amplitudes are accompanied by complex nonlinear dynamic behaviors such as the multivalue and jump phenomenon. The change of current-carrying i has an obvious effect on the nonlinearity of the system. The nonlinear and response amplitudes of the system are also enhanced with the increase in wind velocity. The stability of the system is judged when the primary resonance occurs, and it is found that the response amplitude shows synchronization and the out-of-step phenomenon with the change of tuning parameters. The research results obtained in this paper would help to further improve the theoretical modeling about current-carrying iced lines, and the research of line parameters can give a certain reference value to practical engineering, and it will have a positive effect on the safe operation of high-voltage transmission lines.

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Forced-self-excited system of iced transmission lines under planar harmonic excitations

et al. 2022

Self Cite

View full text Add to dashboard Cite

This paper is concerned with the analysis of the self-excited vibrations and forced vibrations of the iced transmission lines. By introducing the external excitation load, the effect of dynamic wind on the nonlinear vibration equations of motion is reflected by vertical aerodynamic force. The approximate analytical solution of the non-resonance, and the amplitude frequency response relation of the principal resonance of the forced self-excited system are obtained by using the multiple scale method. With the increase in excitation amplitude, the nonlinearity of the system is enhanced, and the forced-self-excited system experiences three vibration stages (self-excited vibration, the superposition form of self-excited vibration and forced vibration, forced vibration controlled by nonlinear damping). Among them, the accuracy of the approximate analytical solution decreases with the increase of the nonlinear strength. And the excitation amplitude is greater than the critical value, the quenching phenomenon appear in the forced-self-excited system, and the discriminant formula is derived in this paper. In addition, the frequency of excitation term determines the vibration form of the system. The principal resonance, super-harmonic resonance and subharmonic resonance of the forced-self-excited system are analyzed by using different excitation frequencies. Compared with the principal resonance and the harmonic resonance, the meaningful transition from periodic response to quasi periodic response is easy to appear with the condition of the 1/3-order sub-harmonic and the 3-order super-harmonic. The conclusions would be helpful to the practical engineering of the iced transmission lines. More important, as a combination of Duffing equation and Rayleigh equation, the forced-self-excited system also has high theoretical research value.

show abstract

Planar Nonlinear Galloping of Iced Transmission Lines under Forced Self-Excitation Conditions

Cited by 7 publications

References 29 publications

Forced-self-excited System of Iced Transmission Lines under Planar Harmonic Excitations

Forced-self-excited System of Iced Transmission Lines under Planar Harmonic Excitations

Investigation on the Nonlinear Vibration Characteristics of Current-Carrying Crescent Iced Conductors under Aerodynamic Forces, Ampere’s Forces, and Forced Excitation Conditions

Forced-self-excited system of iced transmission lines under planar harmonic excitations

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